How recently? I opened an account for my Estonian company as an e-resident (from the EU) in Q1 2019 and it took a grand total of ~40 minutes at the bank to get everything working. I had to visit the bank HQ in person but the whole process was really really smooth sailing.
To be clear, I did that because I wanted the convenience of having Leapin to also have access to my accounts so they'd handle my invoicing and expenses without any significant trouble for me (ie. sending them the account movements periodically). Originally I had an electronic payments account in a Finnish bank and for that I didn't have to travel anywhere but I needed a full bank account so I'd be able to pay dividends into it so I went there. If I just wanted to pay myself via salary I wouldn't have needed to travel there at all but I'd rather my income be via dividends than via a salary because of tax purposes in my country of residence.
That said, I could've used a business account opened in other banks (including outside of Estonia) to do that but I'd be missing out on the convenience that is them having access to the account.
The company's details (which was already up and running and registered in Estonia) which were provided by my accounting services and my e-residency ID. Once there I also needed to provide my national ID card (Portuguese), EU citizens from countries that don't have that would have had to provide a passport instead.
