If your goal is absolutely Big Six, safest bet is to sit tight and upgrade. Keep ALL of your apps meticulously updated as soon as you meet published mins.

Odds are good that this will work out for you over the next 3-5 years or less.

Most of the top majors will hire a few regional FO's, don't bank on it but keep the apps updated because it might be you.

Going to an LCC will likely delay your progression to the Big Six, because they are not impressed by LCC FO time, it holds about the same weight as regional FO time so you might well have to upgrade at the LCC before the top guys call. But at that point you're probably five+ years in making close to 300k... hard to leave. Adding a type rating will increase your app score, but nowhere near as much as 121 TPIC.

So really it comes down to aggressiveness vs. security. If you're hell bent on making top dollar, better make your resume look like what the Big Six like to see. If you'd rather just bag a good job asap and settle in for life, take the first LCC gig you can get.

That all assumes you have a pretty clean record... if you have significant black marks which will be problematic for the big guys, an early move to an LCC might make a lot of sense. Get your seniority and hope for a merger... worst case you still have a good job.