The answer to a previous question suggested life could have the time to begin and evolve on a planet orbiting a blue star if it was at first a binary pair that merged. The technical term is a blue straggler. How could we show this on a world? Stars nearby being low mass is already on the table. If it could be shown through the evolution of the life on the planet, that's a plus
First, they need enough astronomical knowledge to predict the lifetimes of stars.
Then, they need to know the age of their planet. When that turns out to thousands of times longer than the predicted lifespan of their star, they'll know something is up. Further astronomical observations revealing the existence of blue stragglers in globular clusters would then give them the resolution to the apparent paradox--their star must have originally been a close binary.
The age of their planet can be independently determined by examining isotope ratios in certain crystals--notably, zircons. These can trap uranium when they form, but exclude lead. Thus, any lead found in them must be the result of uranium decay post-cooling, which provides a reliable clock on billion-year timescales. (As long as your lead readings aren't thrown off by environmental contamination from tetraethyl lead fuel additives, anyway--and if they are, your aliens can just follow the exact same path we did to developing clean rooms and identifying the harmful effects of lead pollution on the way to dating their world).
An alternative means of having life living under a blue star is that it didn't evolve there, but was transplanted from elsewhere.
The most reliable way of doing this would be to have an interstellar civilisation terraform and colonise a planet. If you want to obscure that, a complete collapse and restart of civilisation can happen in 20,000 or so years, which isn't a significant fraction of the life of a blue dwarf or blue straggler. The lack of fossils and other evidence of evolution would not be conspicuous to this civilisation, since they've never lived anywhere else, but they are likely to notice that life seems to have started fairly suddenly for no obvious reason.
This does not seem workable. Presumably, we start with a planet, orbiting a star in the red-to-yellow dwarf range, and life starts up naturally?
Then another star collides with the primary, forming a blue star?
The most basic problem is that the blue star is blue because it's much hotter than the original star. So the ecosystem of the planet is likely to die of excessive heat.
It also seems likely that the process of stellar merger will be quite violent, with the merging stars producing flares on a scale not seen in a normal system. That may well sterilise the planet.
Further, if the planet was in a low-eccentricity orbit round the original star, perturbations as the second star enters the system and merges are likely to produce a high-eccentricity orbit, producing large variations in temperature. That's going to wreck the ecosystem even if it survives the other problems.