To address audio sync issues, try the following.
In the bottom of your OBS Window, there is a frame/section called “Mixer". Scroll through the list and look for the audio input capture line item (usually a unique name you added when adding the Audio Input Capture Source) and click on the “COG Wheel, or Settings Wheel” on the right. Select “Advanced Audio Settings”.
A window should appear showing you the name of the device, the volume bar, and other various settings. Look for the Audio Input Capture item name you configured, and in the column that says “Sync Offset” input 470ms (for some devices the magic number will be between 470-480).
The video should now be synced to the audio being captured.