Is the truth the best option here?
If you are considering leaving your (otherwise satisfying) job simply because you missed open enrollment, then depending on your circumstances, and how you would define "best," that's likely not the best option.
If you have no dependents and are generally healthy, you may be able to get fairly low-cost insurance from your state's insurance exchange (aka "Obamacare.") Most states allow enrollment for 2020 through January 31st. If your state's open enrollment for ACA has already ended, you may still be eligible because of the loss of your current coverage. It may be worth contacting what ever help your state provides (i.e. a Navigator) to help understand your options. At the worst, you may waste a few minutes on the phone, but at best, you may find you have coverage available.
You can also enroll in private coverage that doesn't meet the minimum essential benefits qualification, although these plans are generally expensive and (per the name) don't offer much actual coverage. These are typically sold as critical illness, limited benefit, or medical discount plans.
If you have children and you're worried about their coverage, CHIP plans (child health insurance) don't have any enrollment restrictions; you can enroll your children any time.
Further, in some states, you may be eligible for coverage through Farm Bureau coverage, or coverage through a health care sharing ministry program (which basically operate like an insurance program, but are run by a church-based organization).
Also, some insurers will actually allow "I forgot" employees to enroll, as a special case - especially if the employer is self insured. Although, in most cases, this is strictly not allowed. But, even though you've gotten a "no" answer, it may not hurt to ask again, or ask further up the food chain. It may also be helpful to ask about COBRA, although I'm not sure "I missed open enrollment" is technically a COBRA-qualifying event (when I worked for a TPA that ran COBRA programs, we didn't specifically send notifications to people who affirmatively opted out of employer coverage).
Finally, if you are under 26, ACA regulations require that you are allowed to get coverage as a dependent on your parent's health insurance. If you are young enough, this may actually be the best option, since adding a dependent to an existing plan is almost always cheaper than getting new coverage yourself. This may even end up cheaper than whatever contribution you had to make to your own employer's plan.
If you do get stuck totally without coverage, you still have options to reduce the cost of any specific medical expenses you incur (if you decide to switch jobs, you may still need to work on some of these avenues before your new coverage kicks in under the new job). Many pharmacies or related businesses offer prescription drug discount programs. Sometimes you have to pay to be a member, but discounts can be monumental - it's not unusual for some drugs to be discounted 50 or 75% under such plans. Also, some drug vendors will subsidize the cost of their medications if you do not have a prescription benefit - since you mentioned in comments that you're on regular medication, you may want to contact the company that makes the drug to see if they can discount it for you. On expensive medications, the difference can be hundreds or thousands of dollars a year.
And if it turns out that you incur other medical expenses (say, you have to go to urgent care because you become ill), you can almost always negotiate on the price. Medical providers are used to getting paid by insurance plans, and those plans negotiate fixed rates based on published fee schedules. These rates can sometimes be significantly lower than the billed rate - a normal office visit may bill at $200, but the provider may be used to getting paid $50 from the insurance plans it accepts. You can use this to your advantage, as an un-covered individual. When you get billed for your services, ask the provider, what would you normally get paid for this service from an insurance plan? Then, offer to pay that amount. Most providers will accept without hesitation.
Also, since you mentioned wanting to start therapy, you may want to contact your employer and determine if they have an EAP (Employee Assistance Program). These programs are almost always available to all employees, even if you haven't explicitly enrolled, and they often fully cover or significantly discount the cost of therapy.
So - in short - if you are otherwise happy with your job, you certainly have options for health insurance coverage that don't involve changing jobs. In fact, it's arguable that changing jobs may be a bad plan anyways - what if it takes you 6 months to find an acceptable job? You'd then be halfway to your next open enrollment anyways.