Assuming this pandemic stuff let's us get back on track, I'm thinking 3-4 years before we make a push to get in. It also wouldn't surprise me if we enter into a decade of darkness type scenario a la the Oilers.
3-4 years before making a push to make the playoffs? In today's NHL, things turn over much faster. Sens have already been tanking for 3 seasons now.
Colorado Avalanche
2016–17 : 48 pts
2017–18 : 95 pts
Yes the Avs already had McKinnon, Rantanen and Landeskog but they didn't have much else (outside of Duchene but the only "player" that trade producted so far is Girard), not even a good prospect pool. The Sens pool is a LOT better at the moment than what the Avs had.
Chabot, Tkachuk, Batherson, Norris, Duclair, Brown x 2, Formenton, Balcers, White, Wolanin, Brannstrom, JBD, Thomson, etc already a lot of good to great young pieces. Like we were saying before the pandemic, it's very hard to answer such question BEFORE the draft, a very very solid draft where the Sens hold 2 top-6 picks and another mid-round first...
So I don't see the scenario you describe happen, unless the Senators suddenly don't know how to draft, but the quality already in the system and how they are positioned in this upcoming draft suggests otherwise. It's up to them to not screw up.
The teams that can't ever seen to progress are the ones that are not very good at drafting.
Melnyk could find a way to screw up everything though. You need a lot of money to run a NHL franchise and the Sens