Per U.S. laws, can a person ever pay a fine to avoid imprisonment?
There are many crimes for which the punishment is incarceration, fine, or both. The answer is yes, there are times when a defendant can pay a fine and walk away. That is in my opinion discriminatory in practice as the poor convicted has no real choice.
Your question appears to mean in all cases, in which that answer is an astounding NO. If you are convicted and sentenced to five years in state prison, you will not have the opportunity to pay a fine to escape that incarceration.
If you want to provide the crime for which you are inquiring I may be able to give you a specific answer, or better yet, look it up in your state's criminal/penal code. I believe all state codes are now online.
A judge in sentencing has a number of options subject to the statute or common law. A fine may be one option, imprisonment another. Others include community service, a suspended sentence or death.
What they choose is (subject to appeal or commutation) what you do. You can't substitute one for the other.
People can be jailed for not paying a fine (see e.g. Supreme Court Ruling Not Enough To Prevent Debtors Prisons).
People complain that this is common, for example,
In America, people are routinely jailed for failure to pay fines.
Cash-register justice incarcerates or keeps on probation many people who are not dangerous, just poor.