It is possible for you to apply for in-country Non-O based on the retirement once you enter on Visa-exempt. If you need more time, 30days tourism extension would be available. But if those 30+30 days are enough for you or not depends on how fast you can sort things out for your visa to apply for it while you still have 15days or more remaining with your stamp.
Your funds have to be transferred internationally for your initial in-country Non-O application, but it doesn't have to be in your Thai bank account for a specific number of days. You can apply for it when you get your money transferred technically.
2months of aging of funds prior to the application day is the requirement for a 1-year extension, not the initial visa.
This is the 'general' requirements list for Non-O retirement in-country. You need to get the latest handout from your local immigration office once you are in Thailand because detailed requirements are immigration-office-specific.
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/9.FOR-RETIREMENT-PURPOSES-50-YEARS-OLD-NON-O.pdf