I think the great leap will come when we can mine and refine metals in space and build the very large ships we would need for deep space travel. Obviously we aren’t going to see anything approaching light speed in our lifetimes. Probably a few hundred years of expanding across our solar system with ships that can achieve maybe 10% of light speed.
I think you're right, but I'd put the timescale at closer to a hundred years hence - IF we can keep from blowing each other up in our petty squabbles back home.
We're in the so-called 'J-curve' of technological development now. The pace of discovery is literally straight up, and accelerating. The only things that can slow it down, are lack of will to push the boundaries forward, or outright suppression of actual advancements.
If we can somehow survive and overcome our specie's violent tendencies, we'll make it to the stars.