Yes, you can always do that, but you cannot hold yourself out as
a CMA. This means that the benefit of passing Part 1 alone is small. Same case
for Part 2, and any time before you fulfill the experience requirement and
become eligible for the certificate.
You can start
looking for jobs as soon as you know you plan to take the CMA. In fact, many
candidates start looking as a way of planning for their futures and just to see
what is available out there. However, I advise against actually applying for
jobs too early. If you have not taken and passed both CMA Part 1 and CMA Part
2, you cannot call yourself a CMA certificate holder.
Furthermore, you have to complete the other requirements by the
IMA and actually receive your certification before you can claim the title.
Therefore, if you are looking for jobs that require the CMA certification, then
you won’t be able to apply for these yet.