The former Manchester United manager was appointed on an 18-month deal in his first job since being sacked at Old Trafford in April.
Moyes has been welcomed by Sociedad players, with the team sitting 15th having upset Atletico Madrid last time out.
Sociedad (nine points) have as many points as 19th-placed Levante, making their meeting with Deportivo La Coruna - who are 17th - vital.
Diego Simeone's Atletico Madrid face another La Liga test on Saturday as Sevilla look to challenge Barcelona.
In the lead up to his team's clash against sixth-placed Malaga, Simeone has been dismissing speculation surrounding his future.
The Argentine insisted he was happy at Atletico, who sit fourth in the table after winning seven of 11 matches.
Top two Real Madrid and Barcelona are also in action on Saturday.
League leaders Real should be too good at Eibar as Carlo Ancelotti's men aim for a 14th straight win in all competitions.
Cristiano Ronaldo has already netted 18 league goals this season.
A win and Real's lead at the top could grow, with Barca hosting Sevilla.
Luis Enrique's men have suffered two losses in their past three La Liga outings and enter the clash after a week that included star Lionel Messi hinting he may leave the club at season's end.
Sevilla sit fifth despite being winless in their past two league matches.
Mid-table sides Athletic Bilbao and Espanyol start matchday 12 on Friday when they meet at San Mames, while Rayo Vallecano host Celta Vigo.
Valencia, sitting third and just three points adrift of top spot, visit Levante on Sunday.
Elche and Cordoba are in the drop zone ahead of their meeting, while Villarreal are looking to end a three-match winless league run when they host Getafe.
Granada and Almeria complete the matchday on Monday.