Is this a photodiode or a thermopile?
I'm going to assume it's a thermopile for the time being, but if it's a photodiode it's going to require different circuits and amplifiers.
I won't draw the circuit out for you but you should be able to figure it out.
1. I'd choose something like the AD8551 or AD8628 which have very low offset voltage and very low bias currents. Low bias currents introduce less error when using large resistnaces in the amplifier. Offset voltages get amplified along with the signal too so if you're after 1uV, then the offset voltage needs to be around that or less. I would use these in a non-inverting configuration for higher input impedance.
2. Use only quiet linear voltage supplies. Really quiet ones. You're trying to measure 1uV so the noise on these regulators shouldn't be much more than that.
3. Only use thin film resistors and C0G/NP0 capacitors for any resistors of capacitors in the signal chain. (less noise and no microphonics).
4. Keep components close, and circuit traces as short as possible.
5. Use ground planes and bypass capacitors on everything.
6. You probably need a PCB shield cover on the board over the pre-amplifier portion of the circuit. I'm not sure.
7. Thermopiles measure the temperature difference so shield it from wind and mount the thermopile in an isothermal block (like a big block of copper, steel, or aluminum) to keep the internal temperature constant.
8. You might need to do things like make guard rings with PCB traces to stop leakage currents from messing with things. I'm not sure.
9. Power it off a battery to test. At least that way you know there won't be noise or ripple from your power supply. Once you know what you have you can try using other things to power the board.
10. Do not power any digital electronics off the linear regulaaor powering the pre-amp.
11. Try placing RC filters on the preamp output. I dont think its a good idea to put them at the input since the signal level is so low but it might also be necessary.
I would first try to see how good you can get it using a soldered surface mount protoboard that has a groundplane using (26-30AWG) self-fluxing magnet wire to make all the connections.
Something like this
https://www.busboard.com/documents/datasheets/BPS-DAT-(SMTpads)-Datasheet.pdf