You are making huge mistakes in the beginning, I am pretty sure too. Easy AI can never get heavy cruisers in 10 seconds, and you don't mention to build your own FREE capital ship. Your first capital ship is free, and helps much. Easy AI does not get the research cheat harder AI gets, and it needs 5 military labs for heavy cruisers, and a research, he can get it harder than you, and I am serious about it.
DON'T BUILD DEFENSES. Just don't do that. Only if you reached the AI and think the frontline world needs some help. Fleet is almost in every occasion much better, so don't stop building ships until you see you have bigger fleet than the AI.
If you sit on your home world building everything there instead of spreading (don't upgrade anything on homeworld, maybe only population limit), instead get nearby planets and build things there. Don't upgrade anything on planets only Civilian Infrastructure to increase population. Instead colonize planets around you, as fast as you can, and every type (volcan, ice too).
Start on a BIGGER MAP... Random medium for 1v1 is good for beginners as it leaves you enough space, but still if you play really inefficient even easy AI can easily kill you. On the smallest map don't be surprised you are beaten in the very beginning.
Build scouts, and use them. Always have an idea about what big fleet your opponent has, and try to keep up. Get his ship's counters and build them.
Easy AI is extremely easy as it even gets a negative income bonus, and AI in this game uses resources in a very inefficient way. If you do only colonizing and build fleet you can defeat it in 100% occasions on all maps.
A horrible mistake new players make: they forget to upgrade newly colonized planet population (named civilian infrastructure) to the level where the underdevelopment tax reaches zero, so you don't lose credits on that planet anymore. Asteroid and dead asteroid needs 1 upgrade, other planets need 2 upgrades for having 0 underdevelopment tax. Other than this they build their colony ships very late, they should be first choices to build, andbuild a capital ship in the first second (you need capital ship factory for it, BUILD IT in the first second and queue your capital ship). Sometimes they also forget to build extractors, these should be queued in the moment you colonize the planet.