I created a custom template that I would like Word to use every time I open the program. Currently, it uses the Normal.dot template. Can the setting be changed so that Word uses my template instead, without my having to open the program, then open another file using my template?

I'm pretty sure it works if you overwrite the Normal.dot file. I would certainly recommend keeping a backup of it first, however.

You can start Word with a different template via the /t command-line switch. See: https://support.microsoft.com/kb/210565?wa=wsignin1.0

You can simply create a new Word shortcut using that switch. That way, you can choose between starting Word normally, or with your template. There is no need to overwrite the Normal template, though you could do so if you only ever want to use your custom template.