I know genital HSV1 can be contracted from unprotected oral sex, but what is the actual likelihood? For example, what is the likelihood when the partner is asymptomatic vs symptomatic, and what is the likelihood if the person contracting it has already been exposed to oral HSV1 as a child? If genital HSV1 is contracted, how long does it usually take to find out? (when would symptoms start to appear)
It seems to me that you are looking for solid risk numbers, which I am afraid might not be available. This is just a summary of the basic facts that play into this likelihood.
For example, what is the likelihood when the partner is asymptomatic vs symptomatic
So-called "asymptomatic shedding", when the virus can be transmitted despite the carrier not showing any sores, is very common in both herpes types.
A good article on this is Asymptomatic Shedding of Herpes Simplex Virus 1 and 2: Implications for Prevention of Transmission. It gives an overview over several studies, for example one where 144 heterosexual couples where only one partner was infected were tracked.
Transmission occurred in 14 (9.7%) of the couples, including 13 in which diaries were maintained during the period when transmission occurred. Although 4 couples (31%) reported sexual contact during the prodrome (1 case) or within hours before lesions were first noted by the symptomatic partner (3 cases), in 9 cases (69%) transmission resulted from sexual contact when the source partner reported no symptoms or lesions
PCR studies found that over 80 percent of people showed asymptomatic shedding, on around 20 percent of the days.
So the likelihood probably wouldn't dramatically decrease just because the infected partner is asymptomatic.
HSV1 in the genital region is becoming more common. It is responsible for between 20 and 40 percent of genital herpes. Part of that increase might be from oral sex, but there is no single likelihood figure that can be attributed to a single instance of unprotected oral sex, at least that I can find.
what is the likelihood if the person contracting it has already been exposed to oral HSV1 as a child?
It's possible. Again, we can't really attach a number to that risk. Even people with genital HSV-1 can be infected with another strain of HSV-1 genitally, afterwards being infected twice.
Whereas the sequential HSV-1 isolates in 11 of the 13 patients studied had the same genotypes, the sequential isolates of 2 patients showed a different genotype. The data suggest that HSV-1-induced recurrent genital herpes can be associated with genital reinfection with an exogenous HSV-1 strain.
Small sample size, but we only care that it's possible at all here.
If genital HSV1 is contracted, how long does it usually take to find out? (when would symptoms start to appear)
This varies, not just by a lot of time, but it even varies whether people ever show symptoms. The incubation period is a few days, but around one third of patients may not show symptoms at all. Even more may not recognize them as a herpes infection. HSV-1 also recurs less often after the first outbreak. This leads to a lot of people not even knowing they are infected. Combined with the asymptomatic shedding of the virus, this leads to HSV being a rather prevalent disease. And not even serological testing is over 90 percent certain to detect an infection. The CDC does recommend that patients who have probably been exposed should be tested, though.
(The part of this answer about asymptomatic shedding is taken from an answer written by me to another question What STDs can be transmitted if both parties have no open sores/cuts )