Q:

Is there a good synonym for "recency"? 

I wasn't sure I had ever used/heard the word recency before but, when trying to come up for a word to describe proximity in time, it popped into my head.  It's in the Merriam-Webster dictionary so I must have come across it somewhere before.  They do not list a synonym.  Is anyone aware of one? 

A:

As far as recency is concerned,  recentness appears to be the only synonym available.      
However, from what I understand from your question, temporal proximity is what fits your need best.      

A:

There are some synonyms, but the choice of which one to use depends on context.  

Novelty
Freshness
Youth

If you want to describe the state of having just happened, recency is your best bet, barring other forms of the same word (recentness and, even more rarely, recentity).