You don't actually need a "warp drive" to get there in a reasonable amount of time. If you can - somehow - invent a drive that'll accelerate you at 1g without stopping for as long as you want, you can get anywhere in the galaxy within your lifetime due to time dilation. To an earth-bound observer, your trip takes approximately 1 year + the distance in light years.

Admittedly it's a big ask. But not as big as bending space.

https://en.wikipedia.org/wiki/Space_travel_using_constant_ac...