Are orbital elements in TLEs valid at the epoch? I want to predict an orbit without SGP, but I need some initial orbital conditions.
Not without a lot of error. The elements in the TLEs are "mean elements", not "osculating elements". i.e. although they have the same names as the Keplerian elements, they are not really measuring the same things. What you can do is evaluate the TLE at epoch using SGP4, and take the resulting Cartesian state vector and transform that via the usual closed-form equations into Keplerian elements.
The short answer is: its not clear**, however, if you have no independent measurements of your own then TLEs will have to do.
If you have some comparable case where you have both your own measurements and the TLEs then you could make a meaningful comparison. Planet labs used to provide both on their website though I can't immediately find the page ++.
The slightly longer answer: its not clear because despite it being intuitively appealing that at the epoch the TLE could effectively rank with a cartesian pos-vel and thus be good for any other propagator model (not withstanding the positional uncertainty of course), there are good reasons to see how the TLE solution has already been subject to propagation with the SGP model, and thus be degraded to an extent.
I have the impression that the published epoch does not necessarily relate to the period of data collection in an obvious way. The following examples are a starting point.
Normal business: If the orbit for an object has been constructed from a set of ranges from one radar or telescope then its easy to imagine that the solved orbit could be published with an epoch somewhere along the arc, or track, of observations, perhaps best where the residuals were least. It could equally simply be the mid-point of the track. The same applies if the orbit had been resolved from two sensors. In any such case the published orbit necessarily involves some use of the SGP propagation between each data point and the epoch.
Privacy: If the sensor's capabilities or operational status are sensitive then I would expect the operator to be a little coy about allowing easy correlation between sensors and resolved orbits. That would be enough to expect some random propagation from the mid-point of a track to the published epoch.
** = Obviously, "validity" depends upon the purpose, which isn't stated in the question. e.g. TLE's are ok for pointing a ground antenna but not for collision avoidance.
EDIT - I found a helpful quote towards this end:
The elements in the two-line element sets are mean elements calculated to fit a set of observations using a specific model—the SGP4/SDP4 orbital model. Just as you shouldn't expect the arithmetic and geometric means of a set of data to have the same value, you shouldn't expect mean elements from different element sets—calculated using different orbital models—to have the same value.
++ Here is the link to the PlanetLabs comparison that I mentioned in my second paragraph: ephemerides.planet-labs.com it provides further links to files giving their own UHF ranging of their satellites and the corresponding TLEs.