Shove
Using the Attack action, you can make a Special melee Attack to shove a creature, either to knock it prone or push it away from you. If you’re able to make multiple attacks with the Attack action, this Attack replaces one of them.

The target must be no more than one size larger than you and must be within your reach. Instead of making an Attack roll, you make a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you.

I would accept this homebrew as an intelligent homebrew for shove:

Shove is Action. If you successfully shove an opponent, you push them 5 + your Athletics skill feet, minimum of 5 feet. So, have Athletics +5, you can Shove 10 feet.

Also, roll double your opponent's roll and knock the target prone as well, thus symbolizing that you caught them off balance.

Anyone who is shoved off a ledge should travel horizontally as normal and then drop straight down. So, if you are 5 feet from the edge and pushed 8 feet, you travel 5 feet to the edge, 3 feet further, and then straight down.

Those who have higher Acrobatics for resisting should have dodge animations for shove if they resist. Those who use Athletics to resist should be shown resisting like American football players smashing into their opponent and not budging. Weapon to weapon or shoulder to shoulder, etc. Shoving back.

And please make knock prone an option. It's one of the ways a fighter can give rogues and other advantage against higher AC enemies.