Time synchronization issues between UART and SRAM

There still must have some sort of clocks to run for both UART and SRAM even though they are asynchronous. Anyhow, with this connection, you should know UART has the baud rate limitation and is relatively slower than writing into the SRAM. To make it higher performance, increasing baud rate is necessary in your case. I would advice you could simulate your design to understand how the data being transferred and time needed.