Why my solenoid valves open only if power is turned on at last?
I don't see any power filter caps on your schematic. A solenoid is a serious load, they are usually listed in ohms. If you don't have a giant cap on your board, you need one. If you connected the 48V to an oscilloscope, you would probably notice the power drop very low.

Another problem you are going to have is solenoids have a high 'on current', you need to make sure you are going to exceed this current and provide enough voltage so the solenoid can turn on. After it turns on you can reduce the current to avoid heating (if you so desire). The switching currents should be listed in the datasheet (which you did not provide).

If you using a cheap chinese power supply, and turning it on to 48V it is going to have some overshoot a few percent above the set value when you turn it on. (I found this anomalous behavior on a student satellite project, it was doing bad things to the software.) This might be giving you the boost your solenoids need to switch on.