Is there a faster way to get heirloom shards?

@FlexinWoods Buying them is fastest.

@FlexinWoods Simply, no
I have been playing since the release. I've been playing quite a lot
I didn't buy every Battle Pass, first one I bought being Season 5 BP

So I got a lot of packs during my playtime, but not a single heirloom apex pack.

Chance for the heirloom pack is I think 0.4%. Unless it's your 500th pack, then it's guaranteed, as you know. So the chance is extremely slim and it's just rng.
So unless you buy Apex packs, there is no real way of speeding up the process or making your chances better
You can go opening 499 packs and still not get a single heirloom, so yeah

@FlexinWoods im level 500+ played day 1 and bought every battle pass and finished entirely. Also spent about $50 on Apex Packs to boot. Still no Heirloom. The fastest way is to throw money at the game, but I don't recommend doing that either.