Answer is No or Yes
No,
because ESRI experience builder is standalone self runing web application build on React.js. Self runing web server is provided by Node.js web server. React.js is build on node.js. You can't break it into parts, assembly into your own existing web page.
Yes,
there is work around, you can use html tag iframe to embed whole experience website into your page. Here is example:
https://transparentgov.net/cleargov1/1734/caltrans-rebuildca-california-department-transportation
Old Project map embeded into rebuild CA parent website
https://rebuildingca.ca.gov/map
New Project map embeded into rebuild CA parent website
https://rebuildingca.ca.gov/map
You have 2 option to embed ESRI map into your existing web page.
option 1.
re-design your entire existing web page with experience builder.
ESRI recommended, but not your best interest. You will be lock into ESRI ecosystem by ESRI's app id, without register ESRI app id for experience builder, you will not be able to run it. You have to pay ESRI storage credit for your website's image, pdf, etc if your experience builder run on AGOL. You are limit to ESRI's login security system, can't use your own login system. Many other limit placed by ESRI.
Here is example
https://experience.arcgis.com/experience/7ea2ca77e22144ff9da18a7af20259e6
More example Like this
https://transparentgov.net/cleargov1/1746/design-your-entire-existing-web-page-with-experience-builder
option 2.
In your existing web page, add ESRI arcgis javascript api,
it is free, almost no impact on your existing web site. Little foot print on your existing web site. But require GIS developer have deep understanding and skills to do the job. Not like experience builder which is no-code COTS off the shelf product, only a few click will setup and run.
Here is example
https://transparentgov.net/cleargov1/1687/does-calfire-map-use-experience-builder-answer-is-no?show=1687#q1687
Here is evidence, it is actually just use Arcgis javascript api v4.20, that is it. No experience builder, no dashboard app.
https://www.fire.ca.gov/incidents#incidentdisclaimer
