God instructs Adam about the tree:

And the LORD God commanded the man, saying, “Of every tree of the garden you may freely eat; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.” — Genesis 2:16–17

Later, Eve talks to the serpent:

And the woman said to the serpent, “We may eat the fruit of the trees of the garden; but of the fruit of the tree which is in the midst of the garden, God has said, ‘You shall not eat it, nor shall you touch it, lest you die.’ ”
— Genesis 3:2–3

The Question says: "I couldn't find where God specifically told Adam that touching it would kill him.".

That's because there is no record of such a conversation.

Here are some possible explanations for this, in order of increasing likelihood:

• Eve deliberately lied to the serpent.
• Eve overheard what God told Adam, but misheard or misunderstood some of it.
• Adam told Eve what God had said, but exaggerated it to make sure she would stay away from the tree.
• God had conversations, other than 2:16–17, with Adam and Eve about the tree, but the Bible didn't record them.

There are many other possible explanations.

But, the true answer wouldn't affect doctrine or salvation, so it's not recorded and is not something we will ever know. We can only speculate about it and express opinions.

Given that there was little to do other than name animals and tend the garden, the tree was by far the most significant thing in their world. It seems highly unlikely that God wouldn't have mentioned it many times on other, unrecorded occasions. He could have even said something like "If you so much as touch the fruit you might die.", just to impress on them how important it was for them to avoid that tree.

We'll never know for sure the details of what did happen, but I think we can be reasonably certain that Eve believed what she told the serpent, and that we have no reasonable grounds for thinking that it wasn't in fact true.

God instructs Adam about the tree:

And the LORD God commanded the man, saying, “Of every tree of the garden you may freely eat; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.” 
— Genesis 2:16–17

Later, Eve talks to the serpent:

And the woman said to the serpent, “We may eat the fruit of the trees of the garden; but of the fruit of the tree which is in the midst of the garden, God has said, ‘You shall not eat it, nor shall you touch it, lest you die.’ ”
— Genesis 3:2–3

The Question says: "I couldn't find where God specifically told Adam that touching it would kill him.".

That's because there is no record of such a conversation.

Here are some possible explanations for this, in order of increasing likelihood:

• Eve deliberately lied to the serpent.
• Adam told Eve what God had said, but she misheard or misunderstood some of it.
• Adam told Eve what God had said, but he exaggerated it to make sure she would stay away from the tree.
• God had conversations, other than 2:16–17, with Adam and Eve about the tree, but the Bible didn't record them.

There are many other possible explanations.

But, the true answer wouldn't affect doctrine or salvation, so it's not recorded and is not something we will ever know. We can only speculate about it and express opinions.

Given that there was little to do other than name animals and tend the garden, the tree was by far the most significant thing in their world. It seems highly unlikely that God wouldn't have mentioned it many times on other, unrecorded occasions. He could have even said something like "If you so much as touch the fruit you might die.", just to impress on them how important it was for them to avoid that tree.

We'll never know for sure the details of what did happen, but I think we can be reasonably certain that Eve believed what she told the serpent, and that we have no reasonable grounds for thinking that it wasn't in fact true.