I always tend to leave Sol in the first year (apart from conventional starts), so a lack of minerals in Sol just adds extra impetus to the exploration effort. It can be a fun challenge to establish an extra-solar mining capability early in the game - keep on eye on your Earth deposits though and don't overbuild.
Alternatively there is the 'Regen Min' button on the System View window (F9), which appears in SM mode. That will reroll all minerals deposits in the system, apart from those bodies that already have colonies (unless I only added that in the unreleased v2.2).