After a longer time, a longer post – sorry
and documents for/about yourself explaining who you are, how you make your money, and so on.
Sure, a personal documentation is expected, naturally.
@johanmichel mentioned just LLC documents, so I've overlooked it somehow.
Bring personal credit card statements especially if your limit 10,000 USD or greater. US banks love seeing someone who not only has money but is spending money in a responsible enough way that they have credit cards with high limit. A high credit limit can sometimes be more helpful than a high bank balance.
This is a
very significant advice. I agree completely and feel a little bit ashamed that I have not recalled this. A high credit limit is really adored in the U.S.
Also bring bank statements for the company's existing accounts,
It will help, definitely. I witnessed opening accounts for LLCs even without banking history, especially with local banks; but if your LLC is not a startup, it's natural to show it.
Chase Bank, Bank of America, Wells Fargo, and Citibank are all known to open bank accounts for foreign-owned LLCs. Doesn't mean they always do it.
Then you have banks Flagstar, MVB, East West, Cathay Bank, PNC, and others that may open an account remotely or in person, but chance of success may depend on where you're from.
From what I have witnessed, a phone call from your registering agent to a local bank representative like “Hey Sam, I have a guy here who is my client for some time and never made any troubles; now he needs a reasonable banking, when can you talk to him?” works really well.
There are banks in California that are very receptive to Asian non-resident entrepreneurs and in Florida (especially Miami) you find ones with a similar attitude towards Latin American non-resident entrepreneurs.
Cannot comment about California (but the abovesaid sounds very plausible); yet re: Florida, Miami especially, banks there are open to Europeans, too – TBMK.
or if other states would be more advantageous
Well, probably it's not an OP's intention to go to states like Kansas or Arkansas; but in general, I am afraid that in the more conservative states not much visited by foreigners it can be more difficult.
Don't be the first to bring up foreign currencies. Wait for them to mention it first, for example if discussing a package that specifically mentions it. You're in America, home of the brave, land of the free, users of the greatest currency the world has ever seen. Your account will support SWIFT in/out but you come across as difficult if you start asking about holding balances in foreign currencies.
Very true.
Sometimes opening a personal account as well as a business account can help close the deal. The bank rep then has double incentives to get you approved.
Yes.
One concern I have is that my funds are crypto-related. While I've had no issues opening bank accounts with this background here in Poland (with full documentation and compliance), I'm wondering if this might be more challenging with US banks?
It depends on the state and on the bank. In general, smaller local banks tend to be more conservative, unfortunately.
I am fine with safer investments... just don't like gambling too much.
This can change the game significantly. If you are able and willing to invest some money like quoted above through the bank, then even some Swiss (or LI) banks can be willing to onboard you, especially if you present your LLC just as a subject managing your assets. Of course, an introducer will help you a lot.
So far I did not see a CAA agent here in Poland.
It is probably not exactly corresponding to the reality as Deloitte & Touche, Ernst & Young, KPMG, PWC and BDO are doing this globally and I guess they have offices in Poland; yet I agree that they are not much likely to help you when you are just a small fish.
Surprisingly for me, there are no independent vendors in PL. Yet e.g. in Czechia I see two and in Germany plenty (
https://www.irs.gov/individuals/international-taxpayers/acceptance-agent-program) – a food for thought

And this Fiverr way discussed above is not that bad, IMO.
Btw, it looks like IBKR will be making an exception and will allow me to transfer funds back into my personal account. That would be the most optimal scenario for me.
Nice to hear – and good for you!
try
Hello everyone,
I'm excited to share that I successfully opened a corporate bank account with Chase Bank remotely without needing an SSN, ITIN, or US residency. The only requirements were an EIN and a zoom call with a banker.
I highly recommend this service for anyone seeking a reliable bank account beyond EMIs, which can shut you down for no reason.
The total cost for setting up the account is $2,000, and a formal agreement will be signed. You will only be charged $500 if the bank rejects your application.
Please ensure that your business is legitimate and does not appear suspicious...
Yes, it has been already mentioned (
@yngmind) and can be a way to go for you, in your situation. You can also check (already mentioned, too) James Baker (
https://jamesbakercpa.com/packages, pay attention to No Travel VIP Bank Account - $2,500).