Letter of no impidedement to marry when no embassy in Indonasia?

Yes the thing to do is to contact the nearest embassy to Indonesia and ask or speak to the relevant government body in your home country or visit immigration or the marriage agency or whatever it's called it's called here and see if they can help.

You have to follow the rules here so don't stop looking for the answer.

I’m I right in thinking your husband to be is “not Indonesian “?
If none of his home country Embassay is within Indonesia its likely he would have to visit another at the Indonesian authorities discretion, for example as of late last year if a uk citizen was to marry in Singapore you had to visit Jakarta for the affirmation (uk citizen) that was a requirement as at September 2017
He would also need all original relevant documents, copies are not permitted, that is accurate as December 2017

I would recommend that he returns to his home country and makes the appropriate arrangements and letterheads, then returns to Indonesia to get married. Sometimes remaining in a host country and requiring the appropriate documentation needs a more baseline approach.  Perhaps marry in the home country and have the legal framework completed in Indonesia. Develop solutions and not add more problems.  👍🏻

I'm unsure which countries don't have a diplomatic service in Indonesia.
I know North Korea has one because I saw the ambassador's car a couple of weeks ago but I only know of one country that has nothing, that being Israel.
If the man is an Israeli, that could cause problems as Indonesia doesn't recognise that country so documents from there, regardless of religion, might not be accepted.
If other countries have no representation the same might well apply, so that must be checked.