I have never seen that CCA is the most important number when buying a new battery. The first number you are looking for is the amp-hours (plus physical size). As the amp-hours already define the volume of the battery, they also roughly determine the CCA.
One you have found a couple of batteries fitting into your car, you may look for one with higher CCA, or even one with same dimensions, but a little more capacity.
Back to your question:
There are no alternatives for cars on the marked, because lead-acid batteries are some kind of unique.
- They can be charged without the need of too much electronics and tolerate overcharging quite well. Finally, apply 14.4V to them, and they will charge until they are full.
- They can be charged very fast.
- They can deliver very high currents for a short time needed to crank the engine.
- They still show a good performance at low temperatures. The CCA is the current the battery can source at -18°C (0°F) for 30s, while maintaining a voltage of 7.2-9V (for 12V batteries).
- They are cheap!
But one also has to say that their capacity/weight or capacity/volume is low (bad)
Looking for a replacement, LiFePO4 batteries are the best option, but they may easily explode when overcharged. They must be monitored carefully during charging, because when they get too warm, they may explode, too...
This is already the problem why you can't just replace a lead-acid battery with a lithium-based one: Because you need additional electronics to charge it.
Further more, LiFePO4 batteries can deliver very high currents for a short time, but each current peak adds some wear to it.
Finally: The price.
I've just found a german shop which indeed sells LiFePO4 batteries as replacement for motorcycle racing sports. They claim a 3.3Ah LiFePO4 could replace a 7Ah lead-acid battery concerning (cold?) cranking amps, but you pay 109€ for it. The lead acid battery is in the order of 40€. However, you also need the full capacity of a battery to supply electrical devices when the motor is not running. The shop sells 7.5Ah for 249€...
You may now scale this up to the size of a car starter battery...
Also, they show lots of impressive data about the cranking performance, but nothing about the life time, which is not so important in racing sports.