Should I pull triplex 4/0 though conduit before laying it in the trench?

Assemble and bury the conduit. THEN pull wire.

You have to fully assemble the conduit, have it inspected if your inspector requires that, backfill it and - important - tamp it, especially the corners. All BEFORE you start pulling any wires into it.

First-time conduit novices always think it will be "easier" to lay all the wire out and thread the conduit sticks over the wire. I do a ton of conduit, and that doesn't sound "easier" at all, it sounds like the most difficult possible way to do it! It really works much better to pull! Of course, if that skill isn't in your repertoire yet, I can understand that -- I myself am terrified of drywall work.

What tends to coexist with the "assemble the conduit around the wires" way of thinking, is also a dastardly plan to build conduit in a way it would be impossible to pull. For instance, using a plumbing elbow instead of a proper sweep, facing the LB against the wall so the access door can't be opened later, etc. That's not allowed, and realistically, you'll hate yourself later if you do it.

Now, if you are using cable that is certified to be used alone (in walls or underground), then it is allowed to use conduit selectively, solely as a damage shield to protect certain segments of the cable run. An example is when you do direct burial, and you are required to use a stick and a sweep of conduit simply to protect the wires on the "Stub-up". In that case yeah, you thread conduit over cable, but it's only a stick or two. If you have used conduit like that before, then I can understand that thinking. And if you want to do that, then simply trench to 26" instead of 21" and just do direct burial. Easy peasy. (however you will never be able to change or upgrade the wire, and that may be a huge problem because...)

Generally, when running conduit the entire route, you want to run THWN or XHHW individual wires. Cables are much stiffer (the same way a ream of copier paper is stiff until you take the wrapper off, then, it's a noodle). This also lets you select exactly the sizes you want, as selection is better in individual wires.

Why are you running triplex anyway?

In almost all cases, triplex is the wrong stuff. Triplex is only allowed between the weatherhead, through the meter, and to the very first breaker or disconnect. Beyond that, everything must be quadplex - separate neutral and ground.

Now some say "But the meter is out at a pole, and this is the run between meter and house". Sure, except didn't the power company/inspector require you to have a main disconnect out at the pole? I bet they did. Then it needs to be 4-wire.