As far as I know you cannot directly assign a hot key to give focus to a toolbar. The only way I managed to get into the search field in the main toolbar only using the keyboard was:
a) Right click in toolbar and choose customize. Rearrange the search field to be in the front of the toolbar. (This step is only needed once and it is only because we want to have to "Tab" fewer times in the toolbar.)
b) Active the file menu with Alt+F.
c) Press escape once to close menu but keep focus in the menu line.
d) Then press Tab key once - now you are in the toolbar. Sadly it wont tab directly into the search field.
e) Use "back tab" (= Shift + Tab) and now you are ready to search.
Too weird an approach though and not quite as effective compared to Ctrl+F to invoke the search dialog.