Immigration can ask for three proofs. Proof of a ticket out of Thailand within the 60 days of your entry. Proof of your accommodation in Thailand. Proof of funds (20,000 thb or equivalent in major currencies) which must be in cash. But Immigration rarely ask for these proofs unless you are a frequent traveller using the visa exempt entry or are scruffy or otherwise suspicious to Immigration. First time travellers to Thailand are almost never questioned but it could happen. But Immigration often asks travellers where they intend to stay.
As your visits to Thailand using visa exempt entries, increase, sooner or later an Immigration official will decide that you are no longer a tourist and will deny you entry.
I have actually used the Doi Saket Bangkok Bank branch to assist a number of people to open bank accouts successfully. Why give away 5,000 thb when not needed.
You should be able to open a bank account yourself, even if you are on a tourist visa or visa exempt stamp. All banks have different requirements. All branches have different requirements. Even within a branch two staff members may give very different answers. Find a branch of the bank you want (I use Bangkok Bank in Doi Saket), in an area with lots of foreigners. Go to the bank with your passport and a friend who holds an account at that branch. Have 100,000 thb to deposit. Should work but many banks/branches will also require a certificate of residence from Immigration. But instead, you could offer a letter from your hotel/ hostel/ Airbnb/ friends house stating that you stay there. Doi Saket Bangkok will work with that.
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Thailand to implement stringent compliance regulations for new bank accounts - Thailand Business News (thailand-business-news.com)