Intel claim this should be by 2025 (once their 18A process comes on line). Obviously they could miss this target, but they say they're still on track.

TSMC managed to leapfrog Intel not too long ago. They still didn’t plan to adopt EUV as recently as 2017:

Not everyone is banking on EUV for 7nm, though. TSMC will extend today’s 193nm immersion and multiple patterning to 7nm, with plans to insert EUV at 5nm - [0]

Chip making is capital intensive, and a new factory that costs to the tune of $20 billions only allows a vendor to stay ahead of the competition for a few years. It’s entirely possible that Intel or Samsung will lead the race at the next technology milestone. They have work cut out for them of course. TSMC has been in the foundry business for a long time.

[0] - https://semiengineering.com/why-euv-is-so-difficult/

Given their current pace, Intel isn't catching but falling behind instead. This has been going on for quite a long time now to be honest.

None of us knows and I haven't seen any projections that Intel's gonna catch TSMC.