Laid off, new offer I don’t love, trying to think through my options

I was laid off by a Big Tech company. I’m still in the notice period or whatever - on the payroll, eligible for internal transfers. I’ve been looking both internally and externally, and I’m not tellin

I was laid off by a Big Tech company. I’m still in the notice period or whatever - on the payroll, eligible for internal transfers. I’ve been looking both internally and externally, and I’m not telling external companies that I’m laid off since I’m still technically employed. I received an external offer, but the money is low and I don’t love the position. I don’t want this job, but I’d obviously prefer it over nothing. I’m considering taking it while I continue to look. It’s a small company and I’m unlikely to run into anyone from there in Big Tech circles in the future. What’s the worse-case scenario if I work there a month or two and then jump ship if I get something better? I wouldn’t put it on my resume or mention it in interviews - I’d continue saying I’m employed at Big Tech until actual separation date for sure, then maybe at that point start saying I was laid off and not mention small company. I would never say I’m working somewhere I’m not, as that crosses an internal line for me and seems easily falsifiable. But can companies find out you’re working somewhere uninspiring instead of being unemployed like you claim? In a systemic way, of course - I’m not worried about some small-world coincidence where someone just happens to know someone.