You have a problem here, namely that asking the user for wallclock time and then finding out the timezone based on that time as a Unix timestamp means that you already need the timezone to convert said wallclock time to Unix.
POSIX/UNIX time is not at all the same as UTC (although they are somewhat related). Unix time measures the time since 00:00:00 1 January 1970 (UTC) in seconds, while UTC uses the proleptic gregorian calendar, with the addition of leap seconds.
It seems to me that what you actually need, is something that converts local time to ‘server time’ (which might be UTC or any timezone offset based on that), so your application accurately knows when an event starts. The Google Maps Time Zone API endpoint isn’t going to help you here, as you actually need the inverse functionality (user picks location + wall clock time, API returns time in UTC or Unix).
