The determination of whether the Church recognizes the marriage as valid belongs to the marriage tribunal, not to the individual hoping to date a person who – at the very least – is still married in the eyes of the state. Ecclesial marriage tribunals will only adjudicate an annulment case after a civil divorce is granted.
Even after a civil divorce is granted, while the divorced person is awaiting a possible judgment of nullity from a marriage tribunal (which will want to look at anything that appears to have been a marriage), that person should not date and others should not accept invitations from that person to date.