The category namer of time-travel debugging, TimeMachine, (hence time-travel debugging in contrast to other attempted names such as reversible, bidirectional, record-replay, etc.) was available in 2003 and supports/supported the ARM7 [2]. Note, that is not ARMv7 architecture, that is the ARM7 chip [3] in use from 1993-2001.
From what I know, the ARM7 was one of the first ARM designs implementing the Embedded Trace Macrocell (ETM) which could output the instruction and data trace data used to support trace probe-based time travel debugging.
[1] https://jakob.engbloms.se/archives/1564
I've thought I bit about how you might support time travel on bare metal embedded - but actually there are hardware-assisted solutions (Lauterbach's Trace32 was one we came across) there sometimes.