1.
promptly, without delay
Doing something quickly or immediately, without wasting time.
2.
right after, as soon as
Used as a suffix after nouns indicating a time or event to mean 'right after' or 'as soon as.' Read as そうそう in this usage.
Usage
Two main patterns
1. 早々に + verb: promptly, without delay (adverbial)
2. Noun + 早々: right after [noun], as soon as [noun] (suffix)
The suffix pattern attaches to nouns representing events or time points: 入社早々 (right after joining), 新年早々 (right at the new year), 到着早々 (right after arriving).
Note: This is different from the colloquial filler word そうそう (meaning 'oh right, that reminds me').