As I mentioned you are able to connect just about anything to the API. You are just limited to 10,000 CMS items.
Not sure how many jobs you are planning on pulling in. But since you are not a developer you may have a hard time doing this not knowing code. Seeing that there are no integrations with Zapier or Integromat at this time, everything will have to be hand-coded to connect the APIs together.
You will need to start here: Redirecting… before you can build out the Job Search API. But yes you can pull in the necessary data.
Would it be possible to show a list of jobs that only my client has on their own page by connecting to Indeed API? It seems that Indeed removed the embed feature so we are a bit stuck here.