The legal deadline is one month from when you enter Spain or from when your residence authorisation is granted (whichever comes later). Article 209 of Royal Decree 1155/2024 (the new Immigration Regulations, in force since 20 May 2025) establishes this obligation.
In practice, the fingerprinting appointment may take longer than a month to become available, especially in large cities. In that case, keep the proof that you requested the appointment as evidence that you are within the deadline.