No, you can't generate own access token on your own (OK, you can. But every proper OIDC implementation will ignore it, because token won't be signed properly by IdP key, so it can't be verified). Access token is always created&signed by Identity Provider (Okta in your case).
However if both clients are in the same realm (realm is a Keycloak term, Okta may use different term - domain, pool, whatever), then they share IdP session. So if user is logged via client_id#1 (IdP session is in place) and you will initiate login procedure via client_id#2, users won't be requested to login again and access token will be issued by IdP in a jiffy*. That is single sign-on feature of OIDC protocol.
*That's not applicable for some special edge cases e.g.: direct access grants was used for client_id#1 login, consent is required, ...