Massive edit: Structure of the question changed.
Yes definitely, you can conceivably go to graduate school. However, if your application isn't competitive for the programs you wish, you might want to spend some time (perhaps a year or two) in an internship, job, or program that helps you build research experience and relationships with people in a position to write you informed letters of recommendation.
To make the most of that time, I would recommend you first reflect on why you've changed your mind and what you really want. Then, try to find job(s) that (1) give you first-hand experience working on the characteristics drawing you to graduate school, to see if that's actually what you want, and/or (2) help you build skills in the specific areas you're interested in, and/or broaden your skills in areas that are widely useful (e.g. computer science).
Some suggestions for how to do this, but these are vague because I'm in STEM but not math:
Check with your undergraduate school/program for career opportunities.
Many (US) schools have networks with alumni or corporate partners. Sometimes you can find a contact to talk to, sometimes you can post a resume. Your school may have resources to get you a job relevant to your degree, that could help you build your application to graduate schools. For many schools, career counselors will meet with you even after your graduate, and might be able to talk to you in person to discuss your situation and your options.
Check with the mathematical societies and associations
Such as the American Mathematical Society, Society of Industrial and Applied Mathematics, etc. Societies like these will often maintain a list of internship/program opportunities that you could apply to, and/or job listings.
Internet search big companies or universities that might be hiring
If the type of math you're interested in lends itself to application in data science, actuarial science, business management, information science, etc, there may be lots of job opportunities where you could apply directly with a Bachelors.
Cold-email professors who might be able to use your skills
Many professors at research-intensive universities will hire lab techs or researchers who are not students. Market yourself as a post-bach looking to build your research experience. (For some professors, this is an easier sell that graduate students, because you're cheaper--or maybe even free--than graduate students and postdocs.) For example, if you're willing to work with a social scientist or biologist, many research groups have lots of data they can't use to its potential, because they lack the mathematical skills to analyze it. (Pro-tip to increase the likelihood of a professor response, attach a CV, and very BRIEFLY state your skills and interest applying your skills to their research; show that you've read and (at least partially) understood the research discussed on their website and any recent publications if you can get ahold of them. Try to keep it as short as possible.)
Or: Apply now and see what happens
If you can afford it, you could apply to a couple schools and see if you get in, go on visits, etc. If you don't get in and choose to take some time and then reapply, keep in mind that some schools will take into consideration if you did apply before. Hence, if you go that route, I would address your background about undergrad, change of heart, applications, and intentional decision to spend time building your skills to make you more qualified for selective programs. This can show a dedication and initiative that many graduate schools in STEM look favorably upon.