It's bolted to the concrete, right?
Sounds like you may be setting up a resonant vibration in the slab itself. If that's what is occurring, you can probably improve the situation by removing the bolts, placing rubber washers both above and below the pump, and rebolting through the washers, so direct bolt to pump contact is eliminated. You may be able to find appropriate washers in the plumbing section of Lowes, etc.
This would be even better: Silicone Sheet, 70A Durometer, Smooth, Red, 0.25" thick, 12"x12" square @ Amazon
You can probably 'test' with pieces of an old thin floor mat, wedged over/under the pump.
If you want a more definitive diagnosis, have someone record a video with your foot on/off the pump, and post it to YouTube. I'm finding that seeing AND hearing makes it much easier for some of us with more experience to figure out what's going on.
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