Paying $1200 for a system that can barely handle any modern title is a poor value. If you are going to spend roughly $1200, get something that can actually handle modern titles. 5600g vs 5700g doesn't really matter, CPU gaming performance wise. Gen 4 vs Gen 3 doesn't matter, for games. I only chose one earlier, because it fit within the budget. A 2tb Crucial P5 would have sufficed, and saved them $100. 16gb is still enough, for now. The used market is always an option, for gpu, but many would prefer to have the warranty of a new card. An 11400 would be better, and doable with $1200, but you would lose out on better upgrade options.
PCPartPicker Part List
CPU: AMD Ryzen 5 5600G 3.9 GHz 6-Core Processor ($238.00 @ Walmart)
Motherboard: Gigabyte B550 GAMING X ATX AM4 Motherboard ($99.99 @ Newegg)
Memory: Team T-FORCE VULCAN Z 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory ($57.57 @ Amazon)
Storage: Crucial P5 1 TB M.2-2280 NVME Solid State Drive ($99.99 @ Adorama)
Video Card: EVGA GeForce GTX 1660 Ti 6 GB XC ULTRA BLACK GAMING Video Card ($565.00 @ Amazon)
Case: Montech X2 Mesh ATX Mid Tower Case ($59.99 @ Amazon)
Power Supply: Corsair RM (2019) 650 W 80+ Gold Certified Fully Modular ATX Power Supply ($74.84 @ Amazon)
Total: $1195.38
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2021-10-14 13:33 EDT-0400
All of this really is a moot point, as the OP was asking for a rig over twice this. If they were not comfortable with spending that much, they wouldn't have put one together for that price. No, personally, I wouldn't buy an RTX 3070ti, or any RX 3000 series card, for that matter, especially with inflated prices. The OP is willing to shell out on one. If they wanted to wait a year, on potato graphics, they would have asked about such a build, from the start. Since they didn't, we suggested builds of a similar cost, but offered more for their budget. Gaming PC costs are a poor value, but you do the best you can, with the money willing to be spent.