Timing of Self Employment quarterly taxes for my startup in mid May

I worked until mid May and was having taxes withheld by that employer.  Then in mid May I started my own business.  I have not paid any estimated self employment or income taxes yet for.  

How should I start?  Wait to pay with Form 1040-ES by September 15th?

Pay an estimated amount for the May taxes asap and then the June through August by September 15th?

Further information, I received a refund for my 2022 income taxes and did not need to make quarterly payments while employed until I went out on my own in May. 

Basically I had planned to estimate my net income from May through August 31st and multiply it times 25% (approximately 10% was my taxes for last year plus 15.3% for self-employment) and pay it by September 15th.

Thanks