Born in Portugalete, Biscay, Basque Country, Veiga played for Athletic Bilbao and Danok Bat CF before joining Real Sociedad's youth setup in June 2014.
[1] He made his senior debut with the latter's C-team on 26 August 2017, playing the last 25 minutes in a 0–2 Tercera División away loss against SCD Durango.
[3] After scoring seven goals for the C's, he first appeared with the reserves on 13 May 2018 by starting in a 3–1 away defeat of Peña Sport FC in the Segunda División B.
[5] He made his professional debut on 3 October, coming on as a second-half substitute for Fabio González in a 4–1 home routing of FC Cartagena.
[7] The following 24 January, he moved to fellow league team Unionistas de Salamanca CF also in a temporary deal.