Is there a shortcut alternative to opening the search engine in a new tab?

Ansive, a possibility is to keep a bookmark of the Google homepage somewhere convenient, such as the bookmarks toolbar.

Or you could place it at the bottom of your bookmarks list so it can be accessed by pressing alt+B then end or up.

Also I believe that you can edit a bookmark to add tags, then you would just need to start typing the tag in the address bar to bring up the bookmark belonging to that tag? (not tested tags myself however)

One final possibility is to enter a dummy character in the search box before pressing enter. So you would press ctrl+K then K on its own then enter.

Just in case you were not aware, your previous Google searches can be accessed via the history (you can see this by pressing ctrl+H to open the sidebar, or ctrl+shift+H to open the history library.)

As jscher2000 has suggested elsewhere, you can press space before hitting enter.

This is neater than pressing the k that I suggested, as the search box in the newly opened page will now be empty (as opposed to having the k or any other character already entered into it).

The other thread is here. It has been suggested that this shortcut was removed deliberately rather than this being a bug? https://support.mozilla.org/en-US/questions/1452133