First of all, you need a Thai bank account in order to be able to apply for the 90-days Non-Imm-O Retirement Visa inside Thailand. You already got a Thai bank account which makes things super easy!
You can apply for the "change of visa type" from the 60-days tourist visa or the visa-exempt entry, to the "90-days Non-Imm-O Retirement Visa", as soon as possible after having opened the Thai bank account.
You need a bank letter confirming that the 800,000 THB are sitting in the account and a proof that they came from overseas.
You need a rental contract and you will need a minimum of 15 days stay permit left on your entry stamp in order to apply.
This application costs a 2000 THB fee, the 90-days visa will be issued for 14 days "under consideration". After 14 days you visit Immigration again and pick up the stamp
And as soon as the money has seasoned in your bank account for two months, you can apply for the "1-year extended stay permit based on retirement" (which some people call "retirement visa" but which is NOT a "visa" but a stay permit). (it doesn't have to be in your account for 70 days, like Ant W Tailor here told you - this was a WRONG advice)
This application costs another 1900 THB fee
Keep in mind, in order to get any service from Immigration, you need to be properly registered in your accommodation by the TM30 registration system
Visit Immigration and askfor the handout list of requirements of the application to the"change of visatype" from a touristic entry to the initial 90-days Non-Imm-O Retirement visa. Open this Immigration website and click onto number 9, this shows the official police order for the "change" . . . . . .
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