Microsoft Office 2016 very slow to start up on High Sierra

That's pretty much to be expected with a rotational hard drive. Once the application code has been cached on the SSD portion of the fusion drive (after the first run after boot) it will start much faster. Pretty much nothing you can do about it without ditching the fusion drive and going to pure SSD.

Unfortunately I think that is about normal (takes about 15 seconds on my 2016 MacBook Pro with Touch Bar that has an SSD). In my case it was about the same with Sierra as it is with High Sierra. You may want to check and/or post to the Microsoft Office for Mac 2016 Word forum: Results in Office - Microsoft Community

It depends on what else is being used. It caches the things it has to load most frequently. Depending on what you're doing, Office is probably getting pushed out of the SSD cache in favor of other code.

The fact is that Office is a bloated mess when it comes to code. Honestly, my first question is how often are you rebooting your Mac? With the exception of days long trips out of town and the odd severe storm warning, the only times I ever shut mine down or reboot it is for updates that require it.

That I can't answer (no experience or knowledge regarding that drive). But the 15 seconds with my SSD still sometimes feels like an eternity. I remember there being a lot of discussion when Office for Mac 2016 was first released and it was even slower then if I remember correctly. I haven't looked for recent discussions in the Microsoft forum.

I don't believe that the 30 second to 3 second difference you are seeing is related to the SSD. My MacBook Pro is all SSD and the first time I start it is 15 seconds. If I quit and then restart it in a short time, it is 3 seconds. If I quit and wait awhile using some other programs, it is back to 15 seconds.

It’s partly Office 2016. With the 16.12 update (and now 16.13), they changed something that causes some of the apps to open very slowly. On my 2010 Mac Pro, under High Sierra on an SSD, any of the apps used to load and were ready to use in about 3 seconds. But as of 16.12, Word will appear on the screen in 2 or 3 seconds, but then stalls doing something. You have to wait another 5 to 7 seconds for the ribbon to be in a ready state (it’s kind of grayed out at first). If you try to open a document while it’s still stalling during its startup, it crashes.

Outlook seems to behave the same as always. PowerPoint and Excel are a bit slower, though not by a lot. But Word is very pokey getting to a ready to use state.

There may also be a combination effect going on. I had updated the OS to 10.13.4, and Office to 16.12 at about the same time. For all I know, the problem may have been caused by the OS update.