I guess you can create a delay by having the pressure plate open a bridge which allows water to active a second plate that closes the bridge and does what you needed?
Nah, it does not work like that: You cannot use a secondary plate to give a CLOSE signal, it will just issue another ON, to which the bridge won't respond as it's already OPEN. At best nothing happens, at worst you'll mess up the whole system with conflicting signals. And you'd need high pressure water to get fast response time. And bridges are sloooooow. Minecarts are much faster for this purpose.
The only exception to this ON/OFF behavior is the gear, which will SWITCH on any incoming signal. So you can build a roller that switches on from a signal from a pressure plate, and off from another. BUT it will switch again 100 ticks later when the plates reset...
What may be possible is to use a plate that opens a 'delaying loop' after the first car passed. Something like this.
WWWWWWWWW
WWWWWTTTW
WWWWWTWDW
WWWWWTPTW
WWWWWTWDW
RRRRRTPTW
WWWWWWWTW
W=wall T=track R=/roller/imp.ramp D=door, P=pressure plate
Minecarts enter from the bottom right, and accelerate to the left. When the first car triggers the first pressure plate it opens the first door so the second car takes the loop before following. I added a second loop on top, so this is good for delaying 3 minecarts actually. Sorry, can't color code the parts.
Also, this design needs 100 ticks to reset (pressure plate default), meaning that if the first cart makes it back to the start any faster then the door won't close, so you'll mess up the timing. You could experiment with the length of the loops to fine-tune it.
But it's much easier to achieve proper timing with the dropping/stacking method: you drop your carts from z+2 high into a chute with a roller at the bottom. The minecarts will be stacked on top each other, and drop down one by one 8 ticks apart as long as the roller is running, which has been tested to be enough to stop jams. AFAIK that's the easiset/fastest method of filling waterguns with minecarts.