Yes, your system can handle the 2080ti, and with the still capable I7 7700k, it will drive pretty much max FPS from the GPU, but maybe a little holdback (bottleneck)
But I'd consider getting a new PSU. The 2080ti at stock settings (not boost) consumes about 260w, it can consume up to 300w at boost frequencies.
Although it's only recommended to have a 650w PSU for a 2080ti, it's rare you whole system would even get close to the 620w you currently have. But, your PSU is prob a few years old now, so advisable to get something more sturdy.
Something like this:
PCPartPicker Part List
Power Supply: SeaSonic FOCUS Plus Gold 650 W 80+ Gold Certified Fully Modular ATX Power Supply ($99.99 @ Amazon)
Total: $99.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-10-03 13:45 EDT-0400