University prestige for tech companies vs HF/HFT firms

I don’t go to a top target school for either tech or finance (think top 20) but have really good GPA and resume. Since I don’t go to a brand name school known for its CS program, do I have a better chance with FAANG or a top HFT firm for its SWE (or quant) positions? I know the latter has harder interviews but in terms of getting my foot in the door with an OA or first interview.