how early can a blood test detect pregnancy?

I'm having bloods done at the hospital as running a fever and elevated heart rate and blood pressure. At 3dpo I have been experiencing extreme hunger, dull low stomach cramps, mild headaches and low dull back pain. Yesterday I had what I think was very light brown spotting/discharge. I'm now 7dpo. We bd every day in fertile window (using opks). So my question is, how early can pregnancy be detected by bloods? As I have made them aware I could have a bun in the oven!!! And I'm an impatient brat 🙃.