If the official i386 arch was built with instructions that your hardware doesn't support, tough cookies
While theoretically possible, that would only happen on processors older than 30 years. Debian's i386 architecture still uses -march=i686 as its baseline compiler target, which is the venerable Pentium Pro: https://en.wikipedia.org/wiki/P6_(microarchitecture)
Not sure why you are downvoted, I guess people don't believe this is true. To confirm: The AMD Geode LX was a <5W 32-bit x86 processor which did not support SSE instructions, and is therefore not fully i686 compatible. According to Wikipedia, it was produced until 2019: https://en.wikipedia.org/wiki/Amd_geode#AMD_Geode
It was used in the OLPC XO-1. The Cisco ASA line of firewalls also used Geode processors at least at some point in its lifetime.
While theoretically possible, that would only happen on processors older than 30 years. Debian's i386 architecture still uses -march=i686 as its baseline compiler target, which is the venerable Pentium Pro: https://en.wikipedia.org/wiki/P6_(microarchitecture)