Hi Myles,
In theory it is possible to replace the front glass but for us home DIY-ers the practical answer is no, you can't. In order to properly do the job, you need a vacuum table to hold the screen, wire guides for separating the front glass, a vacuum chamber to remove air bubbles from the adhesive and finally a UV chamber to harden the glue. Dunno about you, but I don't happen to have any of that on a shelf in my garage.
So yeah, the realistic answer here is that the fix for your phone is to replace the entire screen. The good news is it uses an LCD which is much cheaper than the OLED used on later models, plus it's now old enough that the prices have dropped drastically. Although you can support iFixit's repair efforts by purchasing your screen from them, you can also find it on sites such as Amazon, eBay and AliExpress very inexpensively. I saw one on Amazon for less than $16; at that price it's not even worth considering the idea of messing with trying to do a difficult front glass replacement.
Amazon.com: ZTR Replace LCD Glass Screen Fits iPhone 8 4.7 inch Digitizer Assembly Full Complete Frame Set Display Replacement (Black) : Cell Phones & Accessories
If you did buy yours from iFixit, I'd recommend the Fix Kit version; for an extra $5 USD you get all the tools needed to do the job right, along with the precut screen adhesive needed to put it back together again.
iPhone 8 Screen: LCD + Digitizer Replacement Part, Repair Kit
Either way the procedure for the iPhone 8 is basically the same as that for most modern iPhone models. Here's the iFixit guide showing you step by step how to correctly do the replacement.
iPhone 8 Screen Replacement - iFixit Repair Guide
Good luck; let us know what you decide to do and how it turns out!