Cool game! I really like the concept and aesthetic. I managed to unlock all three periods :-)
Great start screen - it really makes you want to play the game. Although you might want to add the game's title somewhere. Also maybe you could make the time machine sway a little to make it feel like it's moving.
Overall the the gameplay is fun although a bit repetitive. Nice touch with the change from daylight to night. It isn't very clear though how far I need to go to complete a period. Perhaps a distance indicator that reduces as I get closer to the end of the level.
Some buildings in the first period are too tall for the camera and completely obscures the view. The other periods are fine.
The particle effects to show damage on the time machine is great, but it isn't clear exactly how much damage there is, and how close I am to exploding. Maybe add a damage meter above the time machine. Also, I would suggest moving the score to the top screen rather then next to the vehicle.
I hope these suggestions are helpful. Again, great job! I look forward to the next update.