Overheating

When I turn the car on the radiator fans come on immediately and then it’s starts to overheat. I haven’t checked the thermostat and due to rain haven’t had a chance to look at the weep holes on the water pump. The reservoir was empty. I bought it as a project car and just started getting into it. The missing power steering was the first thing I fixed but that’s when I noticed the overheating issue because I drove it a short bit. The point is I find it odd that even cold the fans immediately start. Any advice would be appreciated.