Can blood work determine how long you've had HSV in your system?

I was recently diagnosed with genital HSV1 and I discovered the first "sore" on my genitals two days after oral sex with my new partner. My last encounter with oral sex before my new partner was approx. 10 to 14 days before I noticed my first "sore". Is there a way to tell from blood testing approx. how long the virus was in my system? Neither partners showed any signs of infection on their mouth.