You mostly gotta rely on confessions. Particularly dumb criminals might leave a money trail though (like in Abramski v. US). Also, I think if you gift a gun to

You mostly gotta rely on confessions. Particularly dumb criminals might leave a money trail though (like in Abramski v. US). Also, I think if you gift a gun to someone who isn't legally able to own it, that technically counts as a straw purchase. Different states have different rules/laws for gifting guns (including different rules for different types of guns), which makes your question hard to answer directly.