Using Echo Auto in cars with no Bluetooth and no 3.5mm connection
If your car has no Bluetooth and 3.5mm connection then you have a bigger challenge. If you have no stereo in the car then the easiest option is to get yourself a decent Bluetooth speaker. You might find that something like the UE Wonderboom speaker will work nicely, with the volume and battery life to keep you happy. You just have to connect to the speaker from the Echo Auto during the setup process.
If you don't connect to anything, you can set up the Echo Auto as though your car accepts Bluetooth music via your phone. What that really does it set your phone as the Bluetooth audio device for your Echo Auto and the sound will then come out of your phone's speakers. Whether you'll be able to hear those in the car or not is a separate question.
If you have a stereo there are various other options, like FM transmitters. These will provide a Bluetooth connection for you to connect to and then broadcast over an FM frequency for you to tune your car radio into. Yes, you'll have to find a blank space on the radio tuner, but then anything that it receives will play through your car's speakers.
The downside of an FM transmitter is that they are prone to interference. In reality, if there's the option to change your car's head unit, that's probably going to be a better long-term solution, as well as giving you access to better connectivity. If you have an existing single DIN car stereo and you're doing a simple swap, you'll likely find it's a easy process, but you'll have to check the specifics for your car.
https://www.pocket-lint.com/cars/news/amazon/152634-how-to-setup-your-amazon-echo-auto/