SOFR First started on 26 July. We now have three weeks of data. The results are still somehow mixed.
On the LCH front, the volume is again significantly below the 30 July week level (SOFR First initial week). The volume is roughly the same as at the end of May.
On the ISDA figures side (from US regulatory figures), the absolute volume is up for the 6th week in a row; the volume has tripled in those weeks. But the figures reported by ISDA (USD 166 bn) are well below the figures reported by LCH (USD 520 bn).
A temptative interpretation could be that the US local market is moving slowly to SOFR (SOFR volume is now around 11% of LIBOR volume). Even if that move represents a real chance in behavior, it impacts only a small portion of the USD market. The figures published indicate that ISDA actually captures less than a third of the SOFR market in its SwapInfo analysis.
Note: More volume analysis over the last years available on Marc's multi-curve framework blog.