That CPU is ancient (10/11 generations), and under-powered for real-time video encoding, and a GPU that does NOT support encoding offload from CPU (no NVENC). And 60fps.... ??
The real solution is more appropriate hardware (much newer CPU and/or GPU with encode offload built-in).
Doable at 30fps, with a LOT of care and attention to optimizing both Operating System and OBS Studio, with LOTS of limitations/caveats.
Do you have access to a NVidia GPU with NVENC, like the 1050? if yes, that should really help, though you will still be really CPU limited with only 2c/4t. see
https://developer.nvidia.com/video-encode-and-decode-gpu-support-matrix-new
If you can get GPU encode offload, AND you optimize the Operating System, AND the hardware resource load (especially CPU, but RAM, Disk I/O, etc) are such that there is room (resources for both OBS Studio and whatever you are doing on system), then maybe. For example, if you are gaming or somethign else that is already tasking to CPU, then adding really demanding real-time video compositing on top... not likely to work
And, make sure Disk I/O can keep up. a HDD may be a bottleneck... depends