Play a system that accounts for this.

Fate gives you fate points to spend when you do t like a roll. It also gives you “succeed at a cost” if your fate points are exhausted or not enough.

You can still just roll with it (pun intended) and die to a random goblin if that’s fun. But you also have agreed upon procedure for not doing that. “It looks like the goblin is going to gut me, but (slides fate point across the table) as it says on my sheet I’m a Battle Tested Bodyguard, so I twist at the last second and he misses (because the fate point bumps my defense roll high enough)”

This is pretty easy to import into DND, too, if you like the other parts of it

Rule #1: Maximum Game Fun

I don’t fudge rolls, but I do dynamically adjust enemy’s max HP depending on how well my players are doing.

Fudging removes the joy of surprises and working through failures, or is a band aid to poor planning if failure isn’t an option.

As a DM dice are there to make noise behind the screen and raise tension. They’re a psychological tool as much as they are a randomizer.

Personally I play a lot of World of Darkness games, which runs on dice pools, so if I can just keep obviously adding more and more dice to a pool, recount once or twice and roll to really sell the illusion that they may be in for something a lot bigger and scarier than they are. Or just roll a handful of dice as moments are going on, give a facial reaction and let that simmer under the surface for a while.