The fix is readily apparent. You cannot build a dam across the front, as you won't be able to easily get stuff in and out of the garage. You have to plan for the worst, which is a torrential rain storm. Even a drain might not do it, but will probably solve the problem for 98% of the rain storms.
You can buy pre-moulded styrofoam tapered drain forms. You dig a trench, get it all nice and neat and smooth and square, and set these forms in place. Pour the concrete and pull out the forms. then you just drop in the pre made drain grates you bought with the forms. connect one or both ends to drain pipe to carry the water off to a lower area. Lot of work, sawing the drive, digging the trench for the drain and the pipes, but if done right, it solves the problem.
You will never regret spending money that fixes a problem. You will always regret spending money that half a$$es the job and doesn't fix it.
Charles