Generally not. The only way to tell is if you have previous negative test results specific to the HSV virus. If you do, you know you've contracted the virus since your last test result.

Symptoms of contracting the virus often mimic those of the flu. So, if you have flu like symptoms along with first time sores etc., this can sometimes help determine when you got it. But, some people have the flu like symptoms for every outbreak, and some people have the symptoms with no outbreak - it just goes into hibernation and they think they just have the flu. So this is by no means a fool-proof method of determination.

Incidentally, a doctor might tell you that an IgM test will tell you how long you've had the virus - this is incorrect!! Don't believe it.