You could add two "Run Script" build phases to your Xcode project which runs a tiny script. One at the beginning and at the end of building.
The script at the beginning could literally be something like
#!/bin/sh
date=`date`
# this echo puts the line into your Build Log
echo "time started building is $date"
# and doing a "cat" into some file will save it
cat "time started building is $date" > /path/to/your/buildlog.txt
and the same thing at the end.
You can also do "Pre-Action" and "Post-Action" methods in your Build scheme. They might look like this:
Only here, you'd do the appropriate script thing.