Time dilation is your subjective acceleration veering into more “time” than “space”.

If you somehow were in a flat universe with parallel velocity to an object several light-years away, and somehow managed to accelerate towards it at 1 g, you’d impact at the time on your watch that pure Newtonian physics says you would.

The subjective clocks of the place you’re hitting would measure your travel time as a lot longer, however. But it wouldnt be infinite at all – a relatively small multiple of “several” years, in fact.

(Before the relativistic impact recused both you and them to an energetic plasma, that is.)