What is the smallest time to maturity which I can get the Curve rate for, and how can I get it?
There's a number of ways I can interpret your question. It might be helpful to elaborate on what you're looking to achieve.
If you're looking for Refinitiv zero curve derived from US Treasuries, then the shortest tenor on this curve is 1M. The RIC for 1M point on the curve is USGOV1MZ=R and the chain RIC for the full curve is USGOV1MZ=R.
If the above does not answer your question or does not provide what you're looking for, then please elaborate on what you're looking to achieve.