TL;DNR: Yes, you need to talk to an attorney.
By definition, a trust owns property, which it manages for the benefit of others. (In legal jargon, the property is held in trust for the beneficiaries.) So no, you can't have a trust without transferring ownership.
Three other ways you can transfer property after you die:
1) Will: The most common way to transfer your property to your heirs after you die is through a will. A will is all about carrying out your wishes: It's called your "last will" because it tells your heirs your will as to what to do with your property after you die. Because you get to keep your property, the only paperwork you need to do is writing your will.
2) Joint Tenancy with a right of survivorship: Joint tenancy is the simplest way to transfer property. The name says it all: You jointly own property with your heirs with the proviso that when you die, they continue to own the property. (This is the default for married couples for the property they get during the marriage, where it is known as "community property.") Sadly, you will need to fill out some paperwork to change to this form of property.
3) Transfer on Death Deed: Since 2016, California law has allowed a third option, a "transfer on death deed." This allows you to transfer some kinds of real property (basically, single family homes and small apartment buildings) directly to your heirs on your death. (You can make similar arrangements for many bank and brokerage accounts as well.) Because this is a deed, it involves some paperwork.
Each of these methods of handling your property offers a different mix of costs and benefits. Each is handled differently legally (a will must go through probate, which requires supervision by a court; trusts do not), and may have different tax consequences. Which best suits your needs depends on what you own, where you live, and who you want to get what.
What is to be done?
As you just found out, it is not always easy to figure how best to instantiate your wishes on your own. If you are lucky, someone who knows enough about CA trust and estate law will see your question and take the time to write up a complete and correct answer for you. For many reasons, this probably isn't going to happen. In the meantime, you have two other options. First, you can search for information online. My quick search turned up lots of pages narrowly focused on CA estate law, many with accurate information. Second, you can talk to a lawyer who specializes in CA trust and estate law, to find out what options you have under CA law, and what the costs/benefits they offer you.
My advice would be to skip the searches and call a lawyer. Obviously, YMMV.
Practical advice about advice:
1) You should probably talk to your accountant about the tax consequences of these various approaches to estate planning. Lawyers are not always clear on tax side of estate planning. (Conversely, accountants are not always clear on the legal aspects of estate planning.)
2) Since you hate paperwork, you should not rely on your broker (or real estate agent, or...) for either legal or tax advice. They know much less than they think they do, and can cause big problems. (Even if their bad advice does not cost you $$$, the paper work needed to fix their mistakes can be mind-numbing.)