What components of the counseling process and diagnosis are important in the early sessions with a client?

In the early sessions with a client, a counselor must form a therapeutic alliance with the client. The therapeutic alliance refers to the relationship between the counselor and the patient that will enable the patient to accept the need for change and work towards change. (See source linked below: The Efforts of Therapists in the First Session To Establish a Therapeutic Alliance).
To establish the therapeutic alliance, humanistic psychologist Carl Rodgers believed that the counselor had to show unconditional positive regard for the client and a sense of empathy and understanding. To this end, counselors must empathize with their clients and understand the client's values, motivations, and fears. Without this understanding and rapport, the counselor will not be able to move forward with the work of helping the client.
To make a diagnosis, the counselor carries out a lengthy intake process that involves asking the client about his or her family, work, and mental health history, as well as about the current symptoms or issues the client is dealing with. The counselor must understand all of the variables that are affecting the client at that time, including stresses from family and work, or internal stresses. The counselor must also understand the client's values, background, and culture to be able to form a therapeutic alliance with the client and to make an accurate diagnosis.
https://scholarworks.umass.edu/theses/269/