MacOS – Dell U3415W monitor does not wake when I power up the Mac Mini

I have a late 2014 Mac Mini connected to a 34-inch Dell U3415W display via Thunderbolt to DP. My keyboard and mouse are connected via the monitor's built-in USB hub. There are no other displays connected to the system. I'm running macOS Sierra, but had the same issue in previous versions. I am using full-disk encryption with FileVault.

My issue is that whenever I power cycle my system, the display remains in sleep mode (monitor LED slowly flashes white versus solid white when it's on / Mac LED is solid white). No combination of keyboard presses, connecting/disconnecting peripherals, power cycling the monitor, etc. work.

The only way I can get it out of sleep mode is to type in my password and press enter with the display still blank (power save mode).

I thought of this workaround after connecting a 1280×1024 monitor to the mac alongside my regular 34-inch 3440×1440 display (second display worked). I normally only use the one display though, and it's been about a year since I've hooked up the other one thanks to this workaround. Also, I normally keep the power on so it hasn't been much of an issue.

I'm asking about this now because I recently upgraded to macOS Sierra and was disappointed to discover that the monitor would refuse to wake every time the system went into sleep mode! (not just when power-cycled)

Ultimately, I was able to resolve the sleep mode issue by powering down and unplugging the Mac (I read that this would reset the SMC). However, the issue remains when I power cycle.

Is there a way to make sure that my display always works?

I've speculated that maybe the FileVault boot screen can't handle the 3440×1440 resolution, but that seems like a serious oversight if true. Also, for what it's worth, when I boot up and the OS re-opens my windows, they are all clustered in what appears to be a 1280×1024 box in the upper-left corner of my screen.

How do I make my Mac Mini play nice with my display?

EDIT:

I tried resetting my NVRAM by pressing Command+Option+P+R on startup. I pressed it at about when the first chime occurred and waited for the second chime before letting go. After that, the password screen came up normally!

However, when rebooting (power cycling) afterwards, I still had to type my password into a blank screen. So, the issue is not resolved.

It's odd that a keystroke on startup can make the display wake up normally but that it fails without it.

EDIT:

I tried the HDMI solution below after the issue of my monitor not waking up from sleep mode started happening again sporadically, so the workarounds above were not a permanent fix if anybody was wondering.