When using a team managed (previously known as next-gen) kanban style project, the only way to move issues from the backlog and into the board is to either click and drag that issue into the board section, or right click/use the ellipsis (...) in order to select the 'Move to board' option.
Furthermore when an issues is moved from backlog to board, no issue fields on the issue are uniquely changed here (aside from possibly Rank). Whereas in Company managed Kanban, when an issues moves from backlog to board, the status of that issue changes.
There are no other locations in Jira where you can change what appears on that Team managed kanban board.
It would be great if there was some kind of flag that would appear on the issue data itself to help determine what issues are on the board vs which issues are in the backlog. This could then be an issue field that Automation could set when certain conditions are met. This could be a new custom field, or even if the backlog was a separate status that would then change when the issue is moved to appear on the board.
Customers want to be able to automatically shift issues onto the board. This is possible to do in Company managed projects because a status changes. This is also possible in Team Managed Scrum, because these can use the sprint field in order to set a value in order to make sure it appears on the board.
But this is not currently possible to do in team managed kanban projects.
One way to use automation to move issues from backlog to board is to enable the Sprints feature for this project. This then gives each issues in that project a sprint field that can be set. Automation can then be configured to Edit the issue and set a value for that sprint field. When an issue gains a value to that field, this also makes it appear on the board instead of the backlog view only.