A good way to build gates with limited numbers of transistors is to use RTL (resistor-transistor logic) techniques. For example, here is a NAND gate, which can be converted into an AND gate with an inverter:
The fan-in and fan-out capabilities of this type of logic are not great, which is why it was abandoned once the development of ICs made the incremental cost of transistors essentially negligible. But it can be used to build moderately complex logic circuits if you don't care too much about the speed.
The function of this gate is LOW OR LOW = LOW. From DeMorgan's theorem, I can invert all inputs and outputs and change the gate type, so I get HIGH and HIGH = HIGH.
The image quality is not particularly good. Both collectors go to ground and I have not shown series input resistors. I would probably use about 100 ohms for starters. Both the pullup resistors go to the power rail.