Will artificial grass not feel too solid on a hard floor like concrete?

Can I install it without some sort of padding?

It won't be feeling too solid given the fact of artificial grass fibers provide a lot of softness and cushioning when you step on it. The artificial turf is more like a carpet but a lot of thicker, imagine that you installing regular carpets over concrete surface, you should not have the solid feel, a much thicker artificial grass will make you feel less hard than carpet.

If you would like to have extra cushioning when installing artificial grass, you can always put a layer of shock pad underneath the artificial turf, this will really help to eliminate any hard feel concerns. You can find the details of the shock pad at this link:
https://megagrass.com/products/shock-pads

Any further questions or concerns, please feel free to reach us by filling out this form online:
https://megagrass.com/pages/free-consultation

If you use a shock pad, it won't. It acts as an extra padding to reduce impact.

I'll consider shock pad since it sounds so reassuring that it will add cushion on the artificial grass.

I'm not using anything for cushion but my artificial grass still feels soft.