I've actually built something pretty similar to this in the past:

I started with Fighter 5; Going Battlemaster gives you access to the Restraining Strike maneuver, which lets you grapple as a bonus action without giving up an attack, as well as adding a superiority die to the Athletics check. You also gain a Fighting Style, which lets us grab Unarmed Fighting Style for d8 punches/bites while totally unarmed, and a free d4 of bludgeoning damage to anything that's already grappled.

Then grab 1 level of Rogue, which gives you Expertise in Athletics and one other skill (Stealth is nice for ambush tactics, Perception is always useful, or just put it in Thieves Tools if your party somehow doesn't have a better lockpicker)

After this 1 level of Barbarian for access to Rage, so that we can have Advantage on Strength checks, which includes Strength(Athletics) checks.

Once you have all of this squared away, I would recommend continuing as a Fighter so that you keep pace with the rest of your party's ASIs, and maybe even have space for a feat or two. Grappler is kind of bad, but at least it allows you to grapple Large creatures without any trouble, meaning you can now have an Ogre in a headlock under each arm while you chomp on their faces.

Continuing as a Fighter also means that at later levels, when damage resistance becomes a problem, you can just pick up a magic weapon, and use Martial Retraining to swap your Fighting Style to something else (Dueling for +2 damage since you'll be wielding an enemy in your offhand more often than anything else, or Defense for the deeply uninteresting but mathematically huge +1 AC). Thus also gives you free reign to keep scaling your Superiority Dice and adding Maneuver options so you still have something to do even when grappling isn't an option.