You can control LibreOffice Math without a mouse.
If you want to insert a formula into a text document, and you already know the correct writing, you can proceed as follows:
Write the formula into your text
Select the formula
Choose the command Insert - Object - Formula.
If you want to use the LibreOffice Math interface to edit a formula, choose the command Insert - Object - Formula without any text selected.
The cursor waits in the Commands window and you can type the formula.
You can compose formulas using the Elements pane. Open it with the menu View - Elements if it is not already open.
If the Elements pane is open, use F6 to switch from the Commands window to the Elements pane and back.