There's probably not a specific seniority level in each seat that equates to being able to consistently hold those. I looked at the FOs in the 757 (i.e. the most junior position) for this month. There are pilots in that seat who have been here less than a year who got DDHs (May 2018 hire). The ones who are a little further up the list and actually had a choice of several different DDHs, i.e. it wasn't just a lucky fluke, have been here right around one year. 767 FOs are at about the 3 year point. That will likely improve with that fleet scheduled to double from 60 a/c to 120 a/c, all brand new off the assembly line, over the next 2 years. The other two domestic fleets (MD-11/A300) are in transition, slowly, toward being retired. That's happening at a glacial pace at the moment and will likely last well into the 2020s, but it makes predicting monthly schedule bids difficult. 777 doesn't have anywhere near the same amount of DDHs as the domestic fleets, but if the deadheads are domestic, they're not difficult to get after just a few years. A typical sequence would be DH to Indianapolis, work to Paris and around the world from there, end up in OAK at the end or even back in IND after flying from Asia and DH home from there. Domestically, when a pilot is flying a series of single-day hub turn trips, they can have the equivalent of a DDH week long trip. The line builders or just a pilot using aggressive trip trading can create a DDH week by trading for a front end DH on Monday (or Sunday) and back-end DH on Friday or Saturday. The end result is the same as a week long DDH trip. So, just because you may not be able to hold a true DDH outright doesn't mean you can't create one for yourself if you hawk open time looking to trade.
One note of caution: On any fleet, but especially the 777, putting a deadhead on the front and back of an otherwise shitty trip is the scheduler's version of putting lipstick on a pig. Guys will jump all over those without even a cursory glance at what they'll be doing once they get to their first revenue city and end up finishing the trip with a 1000-yard stare saying their "never agains". DDHs are nice in theory and frequently in practice as well. But, unless we're talking about a small number of "unicorn scenarios", they probably aren't going to make or break your QOL. Holding DDHs to and from one's home airport being the ultimate unicorn.
The actual nuts and bolts of a particular DDH trip are going to determine if it's even something you want to fly. For example - unless you live in a hub city for one of the major US carriers or are deadheading TO one of those same cities, your deadhead is most likely going to be a two-leg event domestically. You live in Nashville or Phoenix and have a DDH in and out of Greensboro, NC. You have to be there on Monday by 1330L. If you're coming from Nashville that's probably doable if you're on the o-dark-thirty, first flight out to Charlotte, DC or ATL to connect to each major airline's GSO flight. Depending on Wx, if you're on probation, etc. you may not feel comfy with that since you probably don't have any back-up options based on the timing, so you decide to leave Sunday and get in position early. FedEx will cover the extra hotel in that situation (if you have extra travel $$) but you're not getting paid until Mon morning when your actual deadhead would have left MEM. Coming from PHX or some other west-ish coast location, you're definitely leaving Sunday. Maybe in either situation, you'd rather be commuting in Monday night on our jump seat to start your first trip out of MEM since you'll have a guaranteed seat on the flight in, commuter protection and less time off the clock commuting.
DDHs or even just front end or back-end DHs can be great enhancements to a commuters QOL, no doubt. But that's going to be highly dependent on each pilot's situation.