When Lelouch made his vow to Suzaku to destroy Britannia this was more of a child venting his frustration at how powerless he was as he was seeing a close friend's homeland be ravaged by the same ideals he thought claimed his mother's life and crippled his sister.
When Lelouch got Geass in his monologue he points out how he was living as a zombie just going though the motions of living but not really living. so between when he made his vow and when he got Geass Lelouch appeared to accept reality that all he could do was look after Nunnally, at least until an opportunity came which would allow him to fight back (which Geass was)
Also i should point out that there was no way the Ashford Family could help him even if he did do something as a child. after Marianne's death the Ashford Family, who were her supports, lost alot of standing.
She is aware of Lelouch's identity as a former prince of Britannia, since her family were close supporters of his mother, Empress Marianne. This relationship however, would lead to the family's nobility status being stripped.
The Ashfords, wanting to restore their former glory, have two options in doing so; either reinstate Lelouch and Nunnally back into the royal family, or to arrange a marriage with a noble. Since the former would get both of them killed, the Ashfords opted for the latter, and arrange several marriage interviews for Milly, with Earl Lloyd Asplund eventually winning out;
Source: Milly Ashford - Character Outline (2nd and 3rd Paragraphs)
The only other thing he could try and do is unify the Resistance Factions but as we could see when he first tried commanding them they weren't fully trusting at first and when things went wrong the second time the group he was commanding abandoned him. really the only reason he gained so much support and fame with the resistance factions was because of his miracles brought on by his Geass
So unless C.C contacted Lelouch much much earlier there was really no way he could put up any sort plan to undermine and destroy Britannia