Post on Facebook Page Using FB Graph API using FB Live but un-reviewed App

I want to post on my own Facebook Page using Graph API. For this, I have created an App.

When App is in Dev Mode, I am able to post on page using Page Access Token with proper permissions. However, the problem here is, the post are not visible to public unless I make the App Live. The posts are only visible to Page Admins.

But as I make my App Live, I am getting below exception from FB APIs.

{
"error": {
    "message": "(#200) If posting to a group, requires app being installed in the group, and \\\n          either publish_to_groups permission with user token, or both pages_read_engagement \\\n          and pages_manage_posts permission with page token; If posting to a page, \\\n          requires both pages_read_engagement and pages_manage_posts as an admin with \\\n          sufficient administrative permission",
    "type": "OAuthException",
    "code": 200,
    "fbtrace_id": "abcdefgh"
}

}

I regenerated the Page Access token after I make my App Live but still above error is coming. I checked some resources which says that I need to submit my App for review. But I don't want to go through that lengthy process.

So, Is there any otherway with which I can post on facebook page using API without putting my App for review process ? Will any other kind of token (i.e. other than page access token) work here ?

Please note, I want to make sure the posts I make to be visible by everyone and not just page admins.