I’ve done similar.
A MOSFET (IRFZ44) was used, the resistors were 100k and the capacitor was 10uF. (need to confirm)
The time was ≈ 1 second.
Add a 68 Ω resistor to your relay if you only have a 5v coil.
Your capacitor is wrong way up.
Maybe experiment with a base resistor added.