Its not clear what you are asking for help with.
Perhaps you are asking how to do 7671 t.tests programatically ?
or you want to talk about the workflow of investigating 7671 variables to elimate unsuitable variables from the analysis before doing any t.tests ?
the short answer is to use one of the purrr::map functions which are part of the tidyverse library to help with iteration. the map function let you iterate over data '.x' and do function '.f' on it. the map variants relate to different ways results can be returned back to you to work with.
In your case the .x would be a list of variable names, so you would extract the colnames() of your dataframe so you could pass this list.
Also in your case the .f would be the skeleton of your function
t.test(Age~PFS_1_yr,mu=0,alt="two.sided", conf=0.95,var.eq=F,paired=F)
however, this would be tweaked so as to be a formula and the PFS_1_yr would be unspecified and filled in by the map function.
This is the general outline of the approach I recommend you investigate.