Can we save our process if we don't save a project?

Yes, you can save either your whole environment or specific objects as .RDS files. RDS files contain one or more R objects. This is very helpful, if you only wish to save intermediate results. For saving RDS objects use saveRDS(). For reloading them use readRDS(). The exact use can be found in the widely available discussions and documentations online. I use it to store large tables that that if read directly from csv-format would take longer to load. Another use for me is storing prediction models that take hours to train.

There are many ways to save results as an R script runs, take a look at the R saveRDS function as one example. For questions like this about R a great place to go is community.rstudio.com.