A:AnswerIt will definitely work with it! Your CPU might bottleneck in some games but it will work. Be wary of the power supply needs though, you should, absolute bare minimum have a 700 watt power supply otherwise it may not work under load.
A:AnswerNow and in the near future, that CPU shouldn't be a big bottleneck in games with the 3060ti - if you can get your hands on it. Depending on what you're looking to do with it, the GPU's useful life is likely to be longer than that of the CPU, so it may be time for an upgrade in a year or two depending on your settings. The main exception would be if you're looking to play at high refresh rates, which means more of a load on the CPU to keep up with drawing all those frames.
See:
https://pc-builds.com/calculator/Ryzen_5_3400G/GeForce_RTX_3070/0Uq1758A/8/100/
They don't have the 3060ti or 3060 yet, but they estimate under a 6% bottleneck on the 3400g/3070 combo with both at stock (neither overclocked). Should be a bit smaller with the 3060ti.
Just please, please make sure you have RAM running in dual channel, and decent sticks at the highest speed they support (may require changing changing a switch in the BIOS - enable AMP). A single stick of RAM, especially running at lower speeds, can cut gaming performance by 10-40%, depending on the game and settings. This applies to any system, but especially if you're trying to squeeze every last bit of performance.