Bulk capacitance equation derivation from appnote
Practically speaking, you could in theory rely on an equation giving the voltage ripple on the front-end capacitor but it does not work like that. What you need to care about truly for the capacitor selection is the rms current in worst-case conditions and the acceptable peak-to-peak ripple current drawn from the power supply unit (PSU). Yes, this input capacitor is to be combined with an inductor to form the front-end \$LC\$ filter.
The design equations are shown below and start with the capacitor rms current calculations. They are coming from the book I published on switching power converters:

These equations give the rms current in the capacitor for this particular application (a 5-V/5-A buck converter). Here, you see that a 2.5-A rms current will flow in the cap. If you are looking for a compact design, you may parallel several MLCC types like those from AVX for which they specify an ESR and a ripple current at 85 °C:

Here, the allowed current is 415 mA per capacitor so I will parallel 7 of them with a bit of margin to form a capacitance of 154 µF and a total ESR of 57 mohms. Once we have the ESR value on hand, we can determine the front-end inductance and find a value of 2.4 µH. In this example, the maximum dc input current will be 2.5 A so the selection of the inductor must account for this value to minimize insertion losses. The peak-to-peak voltage at the buck converter input will mainly depend on the ESR and weakly from the capacitance. That is why calculating the capacitance is a nice theoretical exercise but practically speaking has no value since rms capability at a given operating temperature is what matters in the end.
Finally, a quick simulation of this buck in current mode will tell us if this is correct:

When this is done, you need to damp the input filter to limit its interaction with the negative incremental resistance of the loading converter. You can find plenty of information regarding this extra mile to run in my APEC 2017 seminar. I proposed an alternate method to determine the \$LC\$ filter and it is based on the fundamental attenuation. Don't skip damping or you may run into stability problems later on. Beside the seminar which is kind of heavy lifting, you may want to look at the condensed explanation I gave here.