I'm not sure how suitable it will be for large files, but you try do something like this with Miller
***$ TZ=UTC mlr --pprint --fs tab put -S '$c = strftime(strptime($b,"%Y-%m-%d %H:%M:%S"),"%s")' file
a b c
0 2020-03-03 15:46:52 1583250412
1 2020-03-02 11:05:17 1583147117***
(although I just noticed it appears to screw up the header alignment when the OFS is tab ...).