How do you play against Axe as a pos1?

Archon player. Axe is so incredibly popular as an offlaner in my bracket, so I probably should've asked this question forever ago once I started practicing/maining pos1.

How do you fight against Axe? In all stages in the game.

It seems like no matter what I pick, he does well unless he somehow gets absolutely shit stomped.

If I go some ranged pos1 that tries to avoid Blink-Call like Drow/Muerta, I end up getting hit by it at some point anyway and killed. Usually 3-4 times. All it takes is the smallest mistake in my positioning and I'm just dead.

If I pick some melee pos1 that tries to not get completely ran over during laning phase like Lifestealer/Void/Ursa, I sometimes do okay against him but he ends up running over my team and I still lose.

He just feels impossible to fight if he isn't completely stupid. He's among the hardest offlaners to lane against for me.

Almost every ranged pos1 has a hard time against him (ironically) because after a few levels he can just run at you and shrug off your measely damage and tower damage. If, somehow, he can't, he just starts cutting waves which whittles you down while getting maximum gold and xp.

If I go melee instead, it's a lot more dangerous due to Helix.

It feels like having a competent pos5 is crucial to not getting fucked in the lane, but even then it feels pretty hard for my support because he can just Battle Hunger while losing literally nothing and now my pos5 loses every single trade against the enemy pos4.

Midgame rolls around and now he's got Vanguard (usually), Blademail, Blink and he's stacking Culls and has a lot of armor and it just feels so incredibly dangerous to be anywhere near him.

I'm not trying to reason he's broken or unfair, I just don't know how I should be playing as a pos1 to get around him, to kill him, to survive his oppressive laning phase.