In my view, the premise of the question is itself incorrect. Let us look first at the meaning of selfishness
- devoted to or caring only for oneself; concerned primarily with one's own interests, benefits, welfare, etc., regardless of others.
- characterized by or manifesting concern or care only for oneself: selfish motives.
The supposition of the question, and the explicit statement from the comments, is that anything that does not relate to God is therefore selfish. However, this does not fit the definition.
To take Just a few limited examples. Is a Bhikkhu being selfish? I submit: not. They fail the first commandment, and undeniably this is considered sinful by Christianity, but this is not something born of selfishness. Simply: they have a different view, and are acting accordingly. Disagreeing with Christianity may be classified as sinful, but it cannot be labelled as selfishness. Is a non-Christian aid worker, risking life and injury, a selfish person simply for not following commandment 1?
I accept that many misdeeds are the result of selfishness and/or greed, but the question singles out the first commandment. This, perhaps, is the easiest of the commandments to knock down as being unrelated to selfishness. Let's assume an individual has a working knowledge of Christianity, but was raised in another religion or chooses no religion - this has nothing to do with selfishness as per the word's definition. It is not sufficient to say simply (comments):
One is not saved unless they accept that Jesus is the son of God and that he died for their sins. Not accepting that is also a act of selfishness.
without explaining how non-acceptance is "selfish". I therefore submit that yes: there are things considered sinful that are not selfish in nature. And the question itself provides a prime example.
If we really must add another example - again from the commandments; if I give up a weekend working for someone else's good, without expectation of reward (earthly or divine) - I have violated the sabbath. But no selfish act has been committed.
The commandments around theft, murder, lust, etc do indeed seem likely to have selfish motivation, and so are likely to relate to selfishness. But that then becomes a more circular argument "are selfish actions caused by selfishness?" - to which the answer is : probably! But this does not mean that by extension all sins are selfish. It might be more interesting to ask:
Are all selfish deeds sinful?
I suspect the answer is yes, but I have not considered it comprehensively. But that reversed question is not the same.