Because of how email works, this is entirely impossible.
Your mail client will deliver the message to your server, which will then pass the message on to another server, etc... until finally the message is passed to the destination server. Even then, the target user's mail client needs to recieve and view the message.
Due to this chain, it is impossible to guarantee that a message will be delivered to the final system with any degree of accuracy - also, which is the "final" system? The server or your mail client?
In fact, the whole system incorporates retries, allowing any of the links to fail and for the message to get "stuck" on a server for an undefined period of time.
Finally, as Mokubai as mentioned in comments... time is a tricky topic. All clocks run at different speeds, and while many systems use NTP these days, this still has gotchas - for example, what if the message was delivered at 20:00:00 and 999999 micro seconds... do you include it?
Aside from the synchronisation issues, you have trust issues as soon as you consider using timestamps from other systems.
Mokubai's point of using an "Applications Now Open!" message will solve your problem, because the receiving system has conveyed its state to you, which you can then react to.
You cannot possibly send a message before the window opens, because you've received the notification of the window opening (which took some time to travel to you).
If the window is only open for a short period, or if there is a "race" to get the first message, then I'd suggest that email is not the appropriate tool for the job.