More information required really.

If it’s an ATX board (or derivative of), then momentarily shorting the power button pins on the front panel header will start the board as if there was a power switch.

If it’s an AT (or XT) board then the PSU itself will (or at least should) have a physical mains switch on it, or at the very least will have insulated spade plugs for one to be attached.

There are exceptions to the above, especially if they are from OEMs that deviated from the norm, e.g. my Olivetti PCS 11 that has soft-on even though it’s a 386.

Maybe you can post a picture of the board and PSU. With these we can actually help you any maybe identify the board, but without information on the platform and PSU it's hard to inform you fully.