I know there is a process that backfills badges. So if a badge is added/enabled later on, when it runs, it will award that badge to all users who have the qualifications for it. So I’m fairly certain this one exists… But the trust level one is slightly different. You are likely running into the following bug which makes it difficult to obtain and potentially keep your trust level.
https://meta.discourse.org/t/tl3-posts-read-requirement-seems-to-be-miscalculating/19130