Say, you want to find out the start time of process called 'foobar'. This is what you could do:
ps auxww | grep foobar | grep -v '/bin/sh' | grep -v grep | tr -s '\t' ' ' | cut -f 9 -d ' '
Notice I use "grep -v" to eliminate certain processes that are not relevant. I omit the process that starts foobar ("/bin/sh"). I also omit the "grep" command we are using from the output. If your process is not started explicitly by the shell, you need not do the former, but filtering out "grep" is always useful.
The interesting parts are to the end of the command line. We are looking for the 9th column which has the "start time" of the process. However, since the "ps" output may have multiple tab characters separating the columns, we need to convert multiple tabs to a single tab or a space. Here I have chosen to use the "tr" command to convert multiple repeating tabs to a single space.
Now that we have this handy command, and you are tasked with checking the process start time across a dozen or more machines, it is simple enough to wrap this in a nice one-liner bash loop:
for m in host1 host2 host3 host4 ; do echo $m; ssh $m "ps auxww | grep foobar | grep -v '/bin/sh' | grep -v grep | tr -s '\t' ' ' | cut -f 9 -d ' '" ; done