The Verdict: Clear Path
Your route leads to residence, so you can proceed. Get your accreditation from the national sports council first, then apply for temporary residence under Article 79.6.
Article 79.6 of the migration law gives athletes accredited with the national sports council a temporary-residence subcategory of their own. The years count towards the three that Article 78.1 converts to permanent residence, and towards naturalisation at seven, or five for Central Americans, Spaniards and Ibero-Americans by birth.
The accreditation is handled by the sports body, not the immigration department, so start it first and confirm it before you sign with a club.
Watch for the alternative you may be offered: Article 94.6 covers athletes and performers as a special category, and Article 95 says special categories "no generarán derechos de permanencia definitiva": they create no right to permanent residence, however long you stay. Ask which article your permission will be granted under.