Is it possible to cook bacon without melting as much fat?

I'm not sure this is really a sensible answer… but it's one way…

Deep-fry it.
Should take about 15 - 30s.

That way it will come out even fattier than it went in. Any fat that comes off will be added to the next batch, though probably at an overall loss to the fryer, so you'll have to periodically top back with oil.

Late edit:
I forget the US likes their bacon crispy. My timings were for UK bacon to keep the fat soft but get the meat technically cooked, as the OP asked for 'more fat'.
Crispy I guess will take longer. I've never made crispy bacon in my life & have to assume it's cured differently to be able to make it cook like that.

This is something i've also struggled with. I find that the traditional way of preparing bacon where I'm from (the US) sacrifices flavor and texture for "crunch". This has given me an undeserved reputation for liking "bacon sushi".

I think the easiest route is the "low and slow" method already suggested by pete, but i'd also like to suggest another solution from the almighy J. Kenji López-Alt at serious eats, sous vide it:

1. Drop a package of thick-cut bacon into the water and sous vide overnight (and up to 48 hours)
2. Drain the bacon
3. Heat a cast iron skillet over medium-high
4. Cook the bacon on one side for 2 minutes (pressing on it) and then briefly on the other side for 10 seconds

You can store the sous vide'd bacon in the fridge for a couple of days (since it is fully cooked) and crisp up on demand (true confession: I just eat it straight out of the sous vide sometimes).

I've used this recipe on thinner cuts with some success (although you may want to tweak the crisp step so as not to lose too much fat).

Deep frying bacon is the best. I use a thermometer and keep the oil between 300-350 or it will burn and be chewy. You don't need to cook it dark for crispiness either. cool on paper towel in a metal coriander, it will crisp up as it cools and can always be re-fried if not crispy enough.

to cook bacon with out rendering to much fat from it, choose leaner bacon cuts, lower your heat and use a non-stick pan or cast iron with no oil or butter, nothing. Just the bacon, flipping it constantly. Like every minute or less. thin cut bacon will shrivel, be super wavy, and render a bunch of fat, with crispy tops and chewy inner bumps. thicker cut bacon typically is leaner and render much less fat and will curl less. deli's and cafes drop a press on it. if you do a lot of bacon a press amazing. If you don't do that much bacon, like a pound a week or less, invest in a cast iron skillet and a long steel spatula to press it. the even heat and pressing will give you a more even grill rendering less fat and more even cooking. Again, low-medium heat. I never bacon on high.

For what you want, I think thick cut super lean bacon,on low-medium heat (about 300), on a cast iron skillet or grill plate, with a press or long spatula to press will give you exactly the taste and texture you are looking for. I'm not a fan of oven or microwaves. I'm mean it's good, but not the same.

Cheap thin cut bacon in packages are always going to render a bunch of fat, it's mostly fat. You can go through the packages and try to find packages with less fat. I've seem some cheap packages that are almost all fat. You could also try other uses for the fat. I've bought bacon fat, and it was $10 for a 10 oz jar. Good bacon fat is well over $1 an ounce.

Blalock Lean Thick Bacon Slices https://blalockmeat.com/index.php/store/lean-thick-bacon

steak and bacon presses https://www.amazon.com/d/Cooking-Utensils/Steak-Weight-Bacon-Press-Libertyware

large spatula https://www.amazon.com/Sabatier-5154549-Triple-Rivet-Turner/dp/B0176B7Y18/ref=sr_1_4?keywords=metal+spatula&qid=1565636660&s=home-garden&sr=1-4

Do you care about crispness/chew? If not, it seems to be more common to find raw pork bellies recently. Bacon is relatively easy to cure and needs only curing salt, kosher salt, and sugar and roughly a week in the fridge. Once cured, you can smoke, grill, bake it according to your taste until it is to roughly 140-150F at which point you really do not need to go further unless you want, you can simply slice some off and eat it. It will be a bit chewy, no crisp, but the fat will be mostly translucent but in tact.

If you consider curing your own, this also gives you some other options such as flavoring it as you wish, such as cracked pepper crusted, maple sugar, juice infused such as apple, etc. If cut thicker than normal, say 1/2-1 inch strips rather than slices it can also be cooked either in pan, deep fried or say on a grill to have a crisp exterior but sill have the fat content you are looking for. Curing your own can also give you the option of looking for bellies that are more or less lean to your liking.

This option is admittedly not for everyone, but if you really want superior customized results it is worth considering.

Use thick-cut bacon. Put it into a cold pan, and put the pan on medium heat. Cook slowly until done.

You can also experiment with micro-waving American * bacon. It's somewhat messy, so make sure you use a covered dish to do so. About 2-3 minutes for a slice or 2 gets you started.

But I've found that I can exert more control on the cooking duration because moving/not moving the meat doesn't factor as much.

Note that I don't cook much else in a microwave which I normally find mostly works for reheating, not primary cooking. Except to soften sliced onions before frying them.

* I wouldn't try this with Canadian/UK bacon.