(I present this as an examination of this idea, not a recommendation.)
Attempt to decide based on the spell description if one of them happens slightly sooner
Bludgeoning can happen near-instantly (a shock wave crushing or even ripping material, like in a real-world explosion).
Heat takes a few moments to do its damage. Unless the target creature's flesh is magically heated / turned to char directly, a blast of hot air takes some time to conduct heat into skin. Or into an Iron Golem.
But radiant heat (infrared photons) is absorbed pretty much directly, and perhaps much magical fire damage is mostly from radiant heat, not superheated air. And the speed of light is higher than the speed of a shockwave.
For Meteor Swarm, the description sounds like an explosion.
Blazing orbs of fire plummet to the ground at four different points you can see within range.
So the orbs are of fire, not like a real-world meteorite (a rock which hits the ground really hard). You're not literally getting hit by a large hypersonic rock; that would be even more lethal. (And wouldn't explain applying everywhere in a 40ft radius.) The bludgeoning comes from an explosion as the meteor hits the ground. Most of that is from a one-time shock wave, not ongoing buffeting.
My initial thought was that the fire damage would then follow as fiery air or a wave of magical fire reaches targets.
But the fire damage could easily be mostly radiant heat and be delivered in about as quick a burst as the bludgeoning.
Also, this doesn't explain the spreading-around-corners property. So maybe each Meteor really is 40ft radius, not an explosion in the centre, and smashes all of each area with bludgeoning directly. And also with heat. I'd argue this makes it more likely that the fire damage happens mostly after the bludgeoning.
So overall this reasoning is inconclusive and wasn't very useful. But at least now we've thought about what happens if we attempt this.
I like my other answer better: neither of them are truly instantaneous and instead both happen over some small interval so one type can heal the other type without having to rule on which happens first.