Yup, classic concrete placement failure. 

Can you post a picture from the other side showing you much height you have to work with?

Bung: 
My sister-in-law has found that if the rubber seal isn't touching the ground your house will fill up with mice.

I have a small gap at one end of mine for a couple of extremely annoying reasons, and I get an absolute truckload of crickets coming in if I leave the garage light on after dark.

SomeoneSomewhere:

 

Yup, classic concrete placement failure. 

 

not a failure, it worked as designed.

there was just no forethought put into how it would work with the garage door.

How about trying to buy - or probably get it made - a small 5m Z-shaped flashing that could be fitted (and sealed) to the outside of the bottom edge of the door, reach over the horizontal lip of the concrete floor then go down the outside of the lip. Water would hit the door, run down the flashing and be directed outside, below the floor level.

Helluva lot easier - and probably a lot cheaper - than having a pro remove concrete.

Possibly feasible, but colour-matching the door and actually sealing it against the door is probably going to be a pain. 

The existing lip looks tall enough that taking an angle grinder to it for a horizontal cut should be pretty easy - you get a double step, with a new cut about halfway between the 'outdoor' and 'indoor' levels. 

Here’s a simpler and easier idea. It’s easy to buy aluminium extrusion from Bunnings, M10 etc. Something like a 30x20x1 mm unequal angle - attach to the bottom of the door with pop rivets or whatever. I wouldn’t have thought colour-matching would be an issue here - there would be only a narrow strip of aluminium showing - and it’s basically grey like the door.

It would be dead easy to seal - just run a small bead of silicon or similar sealant along the step in the angle where the extrusion juts out below the door.

This DIY job could be done in less than hour and materials would be less than $50.

Who did you buy the garage off? And did they arrange the entire construction of it?

I bought a Versatile garage 3 years ago and contracted them to build it. They cut in the rebated section of slab for the doorway before the concrete cured, so that water can't track in. My sectional door also has a rubber strip at the bottom which forms a tight seal to keep wind-blown debris and dust out. It's a very neat and tidy job. I can take a photo and post it here tomorrow if you like. They also rebated the pedestrian doorway on an angle so that rainwater dripping off the bottom of the door tracks out and away from the garage.

I would have thought that any concrete placer/garage builder worth their salt would know to do these things as standard.

@eracode - thank you for the great idea. I think this could potentially work with good quality double side tape if I can get something similar. Maybe worthwhile looking at Aliexpress too! 

does your door not have a rubber seal on the bottom of it? why not just put one of those on?

http://www.ravenseals.co.nz/domino/raven/ravenweb.nsf/html-v/catalogue2

They do a couple others which may also suit

Jase2985:

does your door not have a rubber seal on the bottom of it? why not just put one of those on?

http://www.ravenseals.co.nz/domino/raven/ravenweb.nsf/html-v/catalogue2

 

They do a couple others which may also suit

 

 

Wheelbarrow01:

I would have thought that any concrete placer/garage builder worth their salt would know to do these things as standard.