You might be able to, but the OP hasn't had the course where they synthesize filter networks. I suspect that the course instructor is looking for a solution that involves what they have already studied.
Ponder this:
I designed a black box X, shown in the simulations below. In the first simulation, it is driven the way the problem was stated, namely the output impedance of the source is 30Ω, and the impedance of the load is 200Ω. To satisfy the design, the input impedance of of X from In to C should be 30Ω (to match the 30Ω source impedance), and the gain from In (node a) to Out (node b) should be 1. The plot shows that V(a) = V(b)= 500mV (they are perfectly superimposed), so X clearly has unity gain for all frequencies from 100kHz to 10MHz (no phase shift, either)
Why is the voltage at V(a) = 500mV when V2=1V? Well, the only way that can happen is if the input impedance of X (from In to C) is 30+j0, which is what the design asked for.
To check the output impedance of X from Out to C, I moved the source to the other end and drove X backwards 9n the second simulation. Note that V(b) is 500mV, proving that the output impedance of X (which is the input impedance when driven this way) has to be 200+j0 for all frequencies of interest. Also note that V(a)=0, so no signal is passing backwards from Out to In.
Ok, so I have shown you a mystery box X which has the right input impedance, the right output impedance, unity gain going from In to Out, and zero signal passing from Out to In.
What is in the box? Hint, no inductors or capacitors