How can I pair the Samsung PS-WF450 subwoofer to the matching sound bar without the remote.

Question edited for a lot more clarity.
Question moved to a Samsung Sound Bar category.

It is wireless and uses a non proprietary system according to this, so No.

https://eu.community.samsung.com/t5/audio-video/ps-wh550-sub-woofer-compatibility/td-p/3627892

https://www.google.com/search?q=Samsung+ps-wd550+sub

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I suggest turning off and unplugging everything from the power, then disconnect everything from each other. See if you can get it to pair again. Otherwise, please give more details on which model sound bar and subwoofer.
Thank you.

Smash away. I don't think you can connect a wireless piece to a sound bar. This may be out of my wheelhouse, but I don't think so.

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What model is it?

Have you adjusted the subwoofer level? there should be buttons on the remote to adjust this level. Also, make sure you are not in a 'night' surround mode - this drops subwoofer levels a lot

turn the soundbar off, then press and hold the reset button on the back of the subwoofer until the blue light starts blinking fast. the point the remote at the soundbar and hold the mute button until"ID SET" shows on the display. Then turn on the soundbar and it should find the sub and pair with it.

There is a button on the back of the sub that you need to press to complete the pairing..the led will be green when paired successfully or red if it is in standby mode

You will need to take the following steps to ensure that the Vizio wireless subwoofer is working properly:1) You will want to make sure that the subwoofer is in the line of sight of the Vizio sound bar.
2) Ensure the Vizio wireless subwoofer is not beyond 60 ft. away from the sound bar.3) Unplug both the Vizio sound bar and the Vizio wireless subwoofer for 30 seconds and then plug back in.4) Try re-pairing the devices. Pairing works best when you have the devices facing each other about a foot apart during initial pairing, once they are paired you can move them to your desired location.

It could be that the unit is bad, it could also be that the device providing the input is bad. I doubt the cables are bad, but that could be also. Could it be possible that your television has a menu setting that turns the outputs off and on?

Even without the sub, you still get sound through the Bar.

Only way to test it is, different cables, alternate device to provide input for sound.