Four things, in this order: let the AI crawlers reach your site, describe your business in structured data, answer the questions customers actually ask, and point your Google listing at the right place. On WordPress every one of them is a settings box or a plugin rather than developer work.
Start by finding out what is already done
WordPress sites arrive with an SEO plugin more often than not, and Yoast, Rank Math and All in One SEO each handle a real share of this list on their own. Before you change anything, open yourdomain.com/sitemap.xml and view the source of your homepage looking for application/ld+json. If both are there, two of the four are largely done and your effort belongs elsewhere.
This matters more than it sounds. Pasting a second copy of something a plugin already publishes is not neutral: it gives an engine two answers to the same question. What Yoast already does, and what it leaves to you.
1. Let the crawlers in
The heaviest check in the scan, and the one everything else depends on. An engine that cannot fetch your pages answers the question from somebody else. On WordPress the two usual causes are a rule in robots.txt and a security plugin blocking by user agent, and they need different fixes. How to check and fix both.
2. Add structured data
This is what states your services, your area and your phone number in a form a machine will not misread. Paste it into a header code box rather than the theme file editor, which is thrown away on the next theme update. Where the header box is on WordPress.
3. Rewrite your opening lines
The slowest item and usually the one that moves you furthest. Engines lift the first plain sentence that answers the question, so a page opening with company history gives them nothing to quote. What to write instead, and the six questions worth answering.
Then your titles, summaries and headings
Once those four are done, every page wants its own title and summary, one main heading and described photos. On WordPress each is a field. Where they are.
4. Your Google listing
If customers choose you by where you are, your Google Business Profile is quoted about you more often than your own website. The single most common fault we find is a listing pointing at an old site. Check yours.
What WordPress gets right, and what to watch
WordPress is the least restrictive of the major platforms for this work. You have a real filesystem, an editable robots.txt through any SEO plugin, and somewhere to put head code. Nothing on the list is closed to you, which is not true of every builder.
The usual failure is a security plugin. Bot protection blocks by user agent and rarely tells you. It is the commonest reason a WordPress site is invisible to AI answers while looking fine to its owner.
The second is the theme file editor. Code pasted into header.php disappears on the next theme update, and the finding comes back months later looking like a new problem.
The third is caching. A caching plugin will serve the old page for a while after you change something. Clear the cache before deciding a fix did not work.