According to the specs, a USB 3 Gen? Type A cable is supposed to work for both the 5 and 10 Gb/s speeds. What I gather is that the Type C connector is more reliable, and so it is recommended to be sure it works as expected.
The numbering changes have been confusing, but the actual result is simpler. First there was USB (versions 1 and 1.1) which few are still using. Then came USB 2, a newer faster version still in wide use. Then came USB 3. Then came confusion as more refinements were added.
The entire USB 3 system was re-named USB 3.1, and had two speed versions issued. ALL of the USB 3 systems require a new cable type and connectors, but the Type A cable connectors are designed so that you CAN use either type in both USB 2 and USB3 sockets. HOWEVER, you only get the fast USB 3 speeds if ALL of the system - the controller on the mobo, the sockets, the cables and their connectors, and the end device - are for USB 3.
Attempting to make it all easier, they re-named the USB 3 systems again, but without actually changing any big stuff. Now they all are called USB 3.2, but with added details. So there is USB 3.2 Gen1 which can to data transfer at 5 Gb/s. USB 3.2 Gen 2 can do 10 Gb/s. And the latest USB 3.2 Gen 2x2 can do up to 20 Gb/s. That latter normally uses a different mobo header socket called a Type E. And I doubt you can get that data transfer reliably with a Type A connector system. However, that will be hard to test (see next).
When you use such systems to connect to storage drives, other limits come into play. As a starting point, recognize that the USB 3.2 system was intentionally designed so that its is CAPABLE of those data transfer max speeds, but it is expected that right now there are NO devices you can connect that really reach those speeds. So the USB 3.2 systems will NOT be a limit on what your connected device actually does.
For example, the SATA III newest system for hard drives etc. has its own data transfer max of 6 Gb/s. But again, that in itself is deliberately designed to exceed the actual capability of most storage drives. Mechanical hard drives with moving heads on arms and spinning disks can actually deliver data transfer of about 1.0 to 2.0 Gb/s, not even as fast as the previous SATA II design. The very fastest mechanical drive may reach a little over 3 Gb/s, slightly faster than SATA II specs, but not near the 6 Gb/s limit of the SATA III communication subsystem. The closest you may get is a non-mechanical drive, a Solid State Drive (SSD) that will get closer to the 6 Gb/s limit. Now, some SSD's of a different design (the NVMe system) can exceed that, but as far as I know there are no SSD's build to use the SATA interface that can exceed 6 Gb/s max data transfer rate.
So, right now you may get some way to connect a device capable of data transfer over 6 Gb/s, but not over 10 Gb/s. Such a device may come soon, who knows? And when will we see devices able to deliver 20 Gb/s data transfer? Not so soon. One thing for SURE: you will never see a mechanical hard drive able to deliver data over 6 Gb/s - the limits are imposed by the speed of rotation of the disks and the movement of the heads.
Your query is a little unusual, because most recent USB 3.2 Gen 2 devices capable of 10 Gb/s data transfer max are supplied with Type C sockets. Do you really have such devices with only Type A sockets? If so, this unit claims to be an adapter that will convert the Type A female socket into a Type C female socket so you can plug in a cable that ends in a Type C. I do NOT know whether this adapter device actually does what it claims.
https://www.amazon.com/dp/B07Q81GD5G?th=1