While there also were cheap motherboards with 80386SX and no cache memory, most motherboards for 80386DX had a write-through cache memory, typically either of 32 kB or of 64 kB.
By the time of 80486, motherboard cache sizes had increased to the range of 128 to 256 kB, while 80486 also had an internal cache of 8 kB (much later increased to 16 kB in 80486DX4, at a time when Pentium already existed).
So except for the lower-end MBs, a memory hierarchy already existed in the 80386-based computers, because the DRAM was already not fast enough.
By the time of 80486, motherboard cache sizes had increased to the range of 128 to 256 kB, while 80486 also had an internal cache of 8 kB (much later increased to 16 kB in 80486DX4, at a time when Pentium already existed).
So except for the lower-end MBs, a memory hierarchy already existed in the 80386-based computers, because the DRAM was already not fast enough.