You can have trademark rights without registering your trademark. Those unregistered rights are sometimes referred to a common law trademark rights.
You have trademark rights upon using the name, such as by placing the name on your product or by placing your name on your website if you offer services
the mere fact of have an LLC name registered with your state's Secretary of State does not protect you against infringement.
A starting point may be to search whether your logo might infringe another's logo. If it does not infringe, and you want to register your logo without the help of an attorney, go the the US trademark office to complete a trademark application - https://www.uspto.gov/trademarks-application-process/filing-online
One does not necessarily have to have sales of product to establish “use in commerce” to obtain federal trademark registration. But it certainly helps to have sales in order to establish such use.
brand owner can file a trademark application based on an intent to use the brand in the future. Once used, the trademark application can become a registered brand.
Apart for doing a Google search, you might use one of the many vendors that offer trademark searches. These searches can include common law trademarks (i.e., un-registered trademarks).