When I look at teams in a similar position to us, the first one that comes to mind are the Utah Jazz. The Jazz are rebuilding: they have a core of decent yet unspectacular young players, and have had similar picks to us in the past three drafts (14+21/5+23/12). The Jazz aren't tanking anywhere near as hard as teams like the Sixers: like us, they are a team in fringe playoff contention. As a result, they're unlikely to add a franchise player through the draft anytime soon.
The one big difference between us and Utah is that one of their middling assets (the 27th pick in the 2013 draft, which they essentially bought off Denver for just cash) converted into a cornerstone asset in Rudy Gobert. That one stroke of luck is essentially, the only thing that separates them from us. One draft pick exceeding expectations is the difference between being an up and coming young team and being on the road to nowhere like us.
So while it may look like we have no way out of our current predicament, all we really need to make the first step towards progress is for one of our young players to hit. It could be Rozier or Hunter or Mickey, it could be one of the numerous mid-first picks we have this year. If even one of them comes good, we're back on the road to relevance.
I know that all of these middling picks aren't worth a whole lot in trading terms, but put them all together and it would take an extraordinary amount of bad luck for us to not end up with at least one building block. It takes a lot of time and a bit of luck, but so does every other way of rebuilding in the NBA.