Recently, JAXA and Toyota announced that they are developing a self driving rover for the late 2020s, do they have the ability now to launch anything that heavy, or are new rockets and launch centers being developed? Is there any more to their plan about how else they plan to get people to the Moon?
Currently, the largest launcher mentioned on JAXA's website is the in-development H3, which is a medium-lift launcher in roughly the same class as Atlas V or Falcon 9; it could land a very small payload on the moon but probably not a crew-carrying rover, let alone the rest of a crewed moon landing-and-return mission.
If JAXA is planning to land a crewed mission in 2029, they will need something in the Saturn V or SLS class, something more than 5 times the size of the H3. The Saturn V took almost 6 years from NASA's commitment to first flight, and aerospace development tends to be more complicated and time-consuming today, so one hopes that JAXA has a super-heavy lift rocket on the drawing boards today.