I've rarely played the various Indiana Jones games that have come out over the past 40 years (or however long ago the Atari 2600 one was.) I used to try the demos of some of them, back when that was a thing, but the only one I ever played completely was Fate of Atlantis. To me it seemed like there have always been plenty of "Indy"-esque game characters out there, whether Lara Croft, Nathan Drake, or... insert any other characters who might run around the world collecting artifacts, I'm sure they exist and I just can't remember them off the top of my head.
I'm not sure what it would take to get me super interested in an Indy title. Once upon a time I'd have said "Get Harrison Ford to do the voice," but I'm not sure how well he'd manage that now, no offense to him. It would definitely need either the John Williams soundtrack or something similarly thematic. I would definitely like for them to be allowed to use young Harrison's likeness, otherwise it's barely Indiana Jones in my mind and would be disappointing, not unlike that recent Marvels Avengers game that looked more like a "we have Avengers at home" meme.
But yeah, pay Harrison Ford however many gobs of cash he wants for his likeness, render it almost but not quite as creepily close as Moff Tarkin in Rogue One, and give us a blend of "open world exploration" and "epic set pieces worthy of an Indy movie." And figure out a workable whip mechanic. Also only give him a handful of bullets for his gun, so using it matters.
Also, do NOT have him flipping around like Lara Croft. Have him move like an older man who probably shouldn't be doing this any more. (Maybe not Harrison's current age, but slightly older than Holy Grail era.)