Yes, this can be done. One method typically used is to build a small local FileMaker database whose only purpose in life is to open the desired solution on the server. It would have an OnFirstWindowOpen script that basically does that, using an Open File or Open URL script step (see below for format of the URL).
Another option is to use a URL link with the fmp:// link pointing to the database. Such a link looks like this:
fmp://[server name or IP]/database name
Using the latter method also allows you to place a link on a web page, if your company has a page where a link would be convenient for users.