Search Console is a log of what Google fetched. “Not found (404)” on a URL you just published often means the last crawl was before the file existed. Related: website rescue.
404
Put a real page there or 301 to the canonical. Do not redirect everything to the homepage.
Crawled — currently not indexed
Usually thin or duplicate content. Rewrite or consolidate. Do not bulk-request those URLs.
Redirect
Inspect the destination, not the alias. Discuss your project.