If you google "soft bedding a spring air rifle" you will get the same info I posted below.
My new Beeman R7 was just fine out of the box, even better with the Hawke 2-7 x 32mm mil dot scope added.

But I can't leave well enough alone. I decided to get some closed-cell neoprene tape (Home Depot Pipe Insulation $12) and give it a go.
This is reversible so here we go.

I am not the author of this next part
How to Soft Bed Spring Piston / Gas Ram Pellet guns.
Purpose: Floats spring tube metal on a thin, mushy layer of Neoprene up off of the stock wood.
Result: Reduces felt vibration, allows BENCH RESTING on firm sandbags which aids accuracy!

Get 1/8th-inch thick Neoprene. Adhesive backed material (Home Depot)
It's the principal of floating metal off the wood.  Use a box cutter and straight edge to cut 3/8th wide strips, or per your guns stock lands.
Peel paper off sticky back of neoprene strips.
Place strips in bedding channel about 1/16 up from drop-off edge.  It will mush down and fill the gap.
Put Two full length strips in channel (one on each side) leaving a gap back at the trigger from half way between trigger pins to the back of inletting. Small pieces fill back end of inletting leaving gap for cross pin and cut out to allow room for trigger group.
Full SOFT BEDDING COMPLETE Now you need to install the action into the wood.
Use "C" clamp to get front stock screws down far enough to start since they are now sitting on 1/8" of  neoprene. Make sure you don't strip the screws. This is especially tricky when you have cups fitted. Start front stock screw holes first. Then do trigger guard screws.
INSTRUCTIONS AFTER BEDDING

1.  Tighten all screws tight
2.  Let sit overnight
3.  Day 2 -- Morning -- Tighten Again
4.  Day 2 -- afternoon -- Tighten Again -- shoot 20
5.  Day three -- Tighten again -- DONE!
6.  Periodically test screw tightness.

OK... Back to OP

I did this and have shot about 40 rounds. It does make a difference. The gun has more of a dull thud and less metallic "spring in tube".
Is it quieter? Maybe a little
Less felt recoil? I believe so
Do you need to quit work today, run to HD for supplies, and rush home because it's a game changer? No
Is it worth it? Sure why not... I used the rest of the neoprene to insulate a pipe outside by my garden. Again, it is reversible.

Stock, stock
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Neoprene closed-cell adhesive back... in the HVAC area of HD
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Some air rifles benefit from a soft bed or artillery hold, while others do better being held tight.  Both of mine, an HW97 and an LGU like a tight hold and when the wind is down, I can shoot a one hole group at 40 yards with either one.  If you do bed the action, be sure it is removable lest it no workie.

Advance to 1:00   The group starts after I learned the wind and corrected for it.  The 177's get pushed around quite a bit.