Sort of lied about lay off during interview what to do now?

My resume doesn't have specific dates and I basically told the interviewers that I was laid off due to covid-19. Truth is, I was laid off a few months prior and it's been tough finding a job due to covid-19.

I know that they will eventually do a reference check perhaps a background check and I'm afraid that they will find out. I'm not sure what to do at this point. I want to come clean because I don't want to deal with consequence of them finding out in surprise. I feel really good about this company too, and I don't want to lose the opportunity. What should I do?

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