How Sin and the fall Glorifies God
The confirmation of the assumption
The reformer that spent the most effort in making his thoughts fully known about this subject is Jonathan Edwards. He wrote two famous books on the topic:
Although both of these works appear highly philosophical Edward’s derived his thoughts from scriptures and I will try and lay out the very basics.
The basic idea goes like this. God, due to his nature cannot be profited by, or receive any thing from the creature as he is perfect. He can’t suffer loss or gain outside of himself.
Since God is perfection anything ‘good and valuable’ in and of itself itself,
God values it with an ultimate respect. Also since God is infinitely valuable ‘in and of himself ‘God must then be the reason for Creation as he must love himself above all things:
That if God himself be, in any respect properly capable of being in its own end in the creation of the world, then it is reasonable to suppose that he had respect to himself as his last and highest end, in this work; because he is worthy in himself to be so, being infinitely the greatest and best of beings. (The Works of President Edwards, Volume 3, Page 14)
Edwards also notes that it is the final result of Creation that must be the original purpose for it and for all things part of Creation.
Whatsoever thing is actually the effect of the creation of the worlds which is simply and absolutely valuable in itself, that thing is an ultimate end of God's creating the world. We see that it is a good which God aimed at by the creation of the world; because he has actually attained it by that means. (The Works of President Edwards, Volume 3, Page 18)
However these quotes only show the support of you assumption but do not answer the ‘mechanic of how’, so I will not elaborate further.
The mechanics of how – his glory – his working
The mechanics of how is dependent on the ‘what’ we think ‘glory’ is. When we define the ‘glory’ we can define his its is manifested by the Devil, fall, etc.
In describing what true virtue is, or ‘Gods glory’ Edwards says:
true virtue consists in love to being in general
(The Works of President Edwards, Volume 3, Page 95)
Then Edwards clearly defines what he means by stating the proper objects of perfect love:
The first object of a virtuous benevolence is being, simply considered; and if being, simply considered, be its object, then being in general is its object; and what it has an ultimate propensity to is the highest good of being in general. And it will seek the good of every individual being unless it be conceived as not consistent with the highest good of being in general. (The Works of President Edwards, Volume 3, Page 97)
In other words he says perfect virtue, glory seeks to be itself above all things and this is the same as seeking the good of every being. However as Edwards hold the election of the reprobate he adds the limitation of 'unless..' which we should treat as off-topic as this goes to far into speculation about the mystery of election.
Here is the second prime object of perfect love, or glory:
The second object of a virtuous propensity of heart is benevolent being. A secondary ground of pure benevolence is virtuous benevolence itself in its object. (The Works of President Edwards, Volume 3, Page 98)
In other words, not only does pure glory seek to be itself, but its glory is also held in its actual goodness towards any object that it seeks to bless.
From defining this 'ultimate virtue', which is God’s 'glory', he says love to God is evidently what virtue is in us as well:
it is evident, that true virtue must chiefly consist in love to god ; the Being of beings (The Works of President Edwards, Volume 3, Page 101)
He adds that this must lead to an 'enjoyment' and 'rejoicing' as part of the nature of true virtue:
A benevolent propensity of heart is exercised, not only in seeking to promote the happiness of the being towards whom it is exercised, but also in rejoicing in his happiness. (The Works of President Edwards, Volume 3, Page 104)
I will not continue to outline his arguments but from this you can see a reformed framework from which to argue anything about the subject. So to avoid the 17th century difficult langue here is modern English verbiage: God is perfect and perfection must love itself above all things being perfectly benevolent. Therefore, the purpose of all creatures must be to serve the highest benevolence of all creatures to the pleasures of God, for which all things are done to the praise of his glory. We must not imagine that the praise of his glory in any way conflicts with out highest good for all manifestations of God’s glory is to our highest good as the essential property of his perfection, so the more God is glorified only means the more we are blessed as he can’t gain anything from our praise or obedience it is only by these that we obtain the effects of his perfect love towards us.
Regarding the sin, the Devil and the fall specifically: we can see how this reformed faith is worked out. As God will not and can’t suffer any thing but what is for his own glory, seeing that he turns every thing he does to the greater and more illustrious advancement of his own glory, the Devil, the fall, sin, all evil, etc. were included in his decision to create the universe and all things in it. For example we would not know how loving and full of grace God was if a fall did not happen, because only by the fall do we see God was willing to suffer Himself i Christ to save His creation. This properly manifests God's perfection to us, more than if it did not happen. Similarly, we would not know how much God hates sin if we did not see the judgment he has made against it, which again makes his perfections known to us.
The mechanics of how – with respect to providence
Regarding the specific question as it is tied into the words 'predestined', from the wider standpoint of the term he did predestine it all, however, this predestination included some free choice of its creatures fully bound into the envelope of his sovereign will and determined purposes. In the narrow sense of the word, sin can’t be said to be predestined at all, as being part of God’s will, for its very nature is defined by its inherent opposition to Gods will. This argument won due nonsensical and there are no reformers who thought this or taught it.
I mention a narrow and wider sense of ‘predestine’ to distinguish how ‘we’ use the word in English. In the Bible, when Paul says predestined, for example, in Romans 8:30, he used the Greek προώρισεν (proorízō). This comes from two root words (pró) "before" and (horizon) "establish boundaries, limits". Therefore the term ‘predestine’ means “establish unmovable boundaries before creation”. Therefore, it is the wider sense of the word that should be used and we can then answer Biblically in the affirmative. ‘Yes’, God predestined everything to the praise and our enjoyment of his glorious grace Yet as already mentioned, not specifically predestined as he did 'specifically' predestine those souls who would, when all things are complete, enjoy him forever and ever. Our election is a special subset go God's overall general boundary-settings and providential management of all things and we should not confuse the two.
In regards to the 'mechanics of how' this providential boundary-settinh of all things, including those things that oppose God’s will, is managed and maintained by God no man can conjecture, but only believe. At a minimum we can simply say that all things recorded in scripture manifest the mechanics and this, including all the history of God with Israel: where his holy will was revealed, his hatred of sin and opposition to it made know, man’s wickedness, his promise of a Messiah to bring salvation, etc. It also includes most importantly the actual sending of his Son, Christ’s incarnation, death and resurrection. His resurrection is not for himself or 'his own glory' in the wrongly understood selfish sense as though he can be glorified more than his own eternal glory is, but 'for us' whereby we become possessors of the universe. God's glory is simply the manifestation of his perfect love to us by grace, giving him nothing more than he had before creation, but giving everything to us which we did not have. In this way 'all things' work out for our own benefit as God’s grace and our benefit coincide in Christ in an incomprehensible manner. This is partly taken up by this post.