You can't
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.
1The only way to guarantee it would be to have access to their mail server and place the email there directly. There are too many servers, relays and other inserting their own delays to be able to guarantee an exact delivery time. Email should never be used for time critical purposes. This also raises the question of time synchronisation. Is whatever time their system "opens" synchronised to a tier 1 internet time server? If not, or if they do not use a time server at all then you cannot guarantee that their time agrees with your time making this nearly impossible. – Mokubai – 2018-06-20T11:44:45.993
1If this is to work in any meaningful way then they need to send out an "applications now open!" Message that you can trigger on which makes your question moot. – Mokubai – 2018-06-20T11:46:24.417
If it is just someone in HR looking at timestamps on emails, that is controlled by the sending client. Change your system clock and there it is. If someone is reading the actual headers, then it gets harder... – ivanivan – 2018-06-20T12:19:30.777
@Mokubai That's what frustrating me, they only gave me a time, and then you just gotta hope your email magically is the fastest and their own time is configured correctly. – Boyd – 2018-06-20T12:36:54.190
@ivanivan I think they just look at their e-mail client. – Boyd – 2018-06-20T12:36:56.890