Don't say you were laid off, say you left the job to start a new web site, but it's not working out financially. And obviously have a small website ready with a reasonable sounding business idea.
It is totally reasonable for counting being laid off as a red flag, it puts a ceiling on your performance - if you were really that productive, they would have kept you.
The problem with the last part here is that even if it signifies a performance issue at the person's last employer, unless you have exactly the same company culture and exactly the same type of projects it tells you very little.
But there are also many other reasons why otherwise productive team members will be made redundant. E.g. sales are flagging and the company needs to cut cost, and are cutting whole teams because they've already cut the low performers.
It is worth probing a bit of someone has been laid off, but I've personally had to make people redundant who I'd have rehired again in a second while keeping lower performers because they were essential in some way or other, and we couldn't justify making them redundant only to move someone else into their position (even with the ridiculously weak employee protections in the UK that'd suggest it wasn't actually a genuine redundancy; but even places where it's legal, it doesn't mean everyone will do it).
Your suggestion about a project to fill the gap might be worthwhile if the gap is long enough. Otherwise it'll just add new questions about why you're giving up so soon.
It is totally reasonable for counting being laid off as a red flag, it puts a ceiling on your performance - if you were really that productive, they would have kept you.