How I can use OAuth authorize endpoint without fusionauth login UI ?
It depends on which grant you want to use. If you want to use the Authorization Code grant, which is what we typically recommend, then you are going to use the FusionAuth login UI (which can be customized via themes).
If you want to use the password grant, you can build your own UI. There's more on that grant here: https://fusionauth.io/docs/v1/tech/oauth/
If you don't care about using OAuth at all, but just want login functionality, you can use the Login API: https://fusionauth.io/docs/v1/tech/apis/login
If you want SSO between different applications, however, you need to use the Authorization Code grant. You are right, there's other related functionality (cookies, etc) that is required for SSO that is managed by the FusionAuth UI (often called the "hosted login pages").
There's an open issue: https://github.com/FusionAuth/fusionauth-issues/issues/1515 to allow for more management of the SSO session via API. Please feel free to upvote this issue and/or add your use case to the comments, as that helps us with our roadmap planning.