Why can't I have enough crema with my espresso machine? Doesn't it provide enough pressure? It seems my machine doesn't create enough pressure because I can't create a decent crema.

The machine heats up water which increases the pressure and eventually the water makes it through the coffee.

I tried compressing the coffee so it's more dense and more difficult to penetrate. 

This lead to a longer time till the first drops of coffee started pouring but still no crema.

My coffee machine is a Krups 872-42 Bravo Plus:
First things first, the ingredients of the crema is partly the answer of this question.

The foam on top of any coffee beverage (espresso, Turkish, aeropress or any other) is formed simply the same. A lipid/water emulsion forms the outer sphere and some gas is inside this sphere. All these spheres stick to each other with tiny coffee bean fragments invisible to human eye. Let's focus to the gas. The gas is mostly Carbon dioxide that is produced during the Maillard reaction when the coffee beans are roasted.

Ok, now we know the chemistry behind. There are three (actually four, but water is there all the time) main contents for our recipe to produce crema:


Lipids
Coffee bean fragments
Carbon dioxide


Lipids and Carbon dioxide are formed by roasting. Fragments are the very very fine powders emerge as the side product of grinding. Fragments don't leave the ground coffee. Lipids, too. But, Carbon dioxide flies away in time.

Normally, after roasting the beans, it is better to wait for two to four days (based on many criteria just like bean type, roast level, brewing technique, etc.) for the Carbon dioxide level of the roasted beans to settle. Then, the flavor of those beans will be delicious. After that time, Carbon dioxide fades away and the roasted beans start to stale.

As you can reason, if your beans have less Carbon dioxide, your final cup of coffee would have less crema. If you have freshly roasted (e.g. 3-days old) coffee, your final cup of espresso would have a thick foam.



It is also known that water pressure affects the crema volume, but should not affect as much as you mentioned here. Even at 7 bars, a decent crema forms according to this study.

And a note, if your machine has difficulties producing enough pressure, more tamping will probably results over-heated water flowing very slowly through the grounds, causing them to burn and all of the lipids to evaporate, could not form the spheres of the crema. As a result, you probably worsen the crema production, coffee odor fills the room but you cannot drink that flavor. Now, all you'll get is boiled coffee juice.

TL;DR The amount of crema is mostly correlated with the freshness of the coffee, not the pressure.