Chauvin didn't need to prove anything. The prosecution, for the murder charge, needed to prove that Chauvin's actions were either "eminently dangerous to others and evincing a depraved mind, without regard for human life" or "without intent to cause death, proximately causes the death of a human being by, directly or indirectly, unlawfully selling, giving away, bartering, delivering, exchanging, distributing, or administering a controlled substance classified in Schedule I or II".
The second half of that doesn't apply to Chauvin (though it may have applied to Morris).
That is the state requirement for 3rd degree murder.
For second degree murder, which Chauvin was also found guilty of, the state needed to prove that Chauvin was either in the process of committing a felony or was "intentionally inflicting or attempting to inflict bodily harm upon the victim, when the perpetrator is restrained under an order for protection and the victim is a person designated to receive protection under the order.".
Chauvin was using a normal restraint technique, called the EMTs, called to expedite the response of the EMTs and did not do anything that could reasonably be considered to intentionally inflict bodily harm.
At most, Chauvin was guilty of "culpable negligence whereby the person creates an unreasonable risk, and consciously takes chances of causing death or great bodily harm to another" which is the manslaughter statute.
The jury went WAY overboard in this case and it is quite possible that the reason they went so far overboard is because:
a. Like you, they believed that Chauvin needed to prove his innocence
and/or
b. They were totally swayed by the political narrative surrounding the whole incident.
For reference -
https://www.revisor.mn.gov/statutes/cite/609