In Star Trek: Discovery 1x06 "Magic to Make the Sanest Man Go Mad", why did Harry Mudd's first attempt to take over Discovery involve him going guns-abalazing? We see on later attempts that his plan of attack is to teleport on board the ship and then covertly sneak around. Why not do that during the first attempt? Why bother shooting people up the first time?
The sneaking approach only worked because Mudd had knowledge he acquired from forcing his way aboard: how to access the computer system, how to get the information he needed, where people were, and so on.
You can imagine the loops worked something like this, ignoring the possibility of previous, unseen loops where he doesn't get aboard:
Loop 1: Harry blasts his way through the landing bay, taunts Lorca on the comms, because he knows he isn't going to be getting much further, is quickly overcome by security.
Loop 2: Harry quickly blasts his way through the personnel he knows are in the landing bay, begins accessing the computer. Because he knows where his targets are ahead of time, he goes through them faster, and has a few more minutes before security shows up.
Loop 3: Harry repeats Loop 2, now knows something about the computer through trial and error, and is able to access it further before he's caught/killed.
Loop N1: Harry has now learned enough about the computer to access it gain some control. He starts figuring out how to get aboard without alerting anyone.
Loop N2: Mudd knows how to beam aboard undetected and the routine of people to move around unnoticed.
Loop N3: Mudd now can get aboard, take control of the computer, and move around undetected.
And so on.
However, none of that works without that first initial step: getting aboard the ship. Without forcing his way aboard he doesn't know where he can beam in to be unseen, how he can beam in undetected, or how to control of the computer to remain undetected.
Because the kind of sneaking Mudd does requires foreknowledge of the movements of people on the ship. Traditional sneaking is slow and methodical because you don't know if there's going to be someone around any given corner.
The kind of sneaking Mudd does is more similar to a video game where all the enemies spawn at pre-determined locations. You might want to 'sneak' through the level without engaging a lot of enemies, perhaps to conserve ammo or whatever, but if you can just quickly reload from a checkpoint, it might make sense to just run through as much of the level as you can on the first attempt to get as much information about where things are as you can.