Start with ownership and indexing
After the owner publishes, verify the property, submit the sitemap and inspect the homepage, product pages and blog hub. A submitted URL is not the same as a guaranteed indexed URL.
Read query patterns
Look for questions with impressions but few clicks, pages that appear for an unexpected topic and terms that reveal a missing explanation. Use those patterns to improve titles, answers and internal links.
Keep a change log
Record what changed and when. Search performance moves for many reasons, so a dated log helps separate a content improvement from a seasonal or technical change.