You've started looking around on data science job websites, but they're all looking for senior level positions
You've started looking for a Junior Data Science job on job websites. Almost all of the jobs you've found posted are from organizations who are looking for senior level data scientists. While you're confident that you shouldn't have any problems learning some new things and are currently learning everything you can about data science, you are looking for a junior position not a senior position. The problem you're running into is that it's hard to find junior data scientist jobs.
Senior Data Scientists need Junior Data Scientists
Due to the nature of the job and the growing need of data science, most companies are currently hiring senior data scientists to start or build out their small data science teams. This is what makes it hard to find junior positions. On the other hand however, once a company has hired senior data scientists, the next logical step is to fill out their team with junior data scientists to help shoulder the important work that the team is doing. Whether helping with general coding, data architecting, data engineering, mathematical modeling, or other things, a Senior Data Scientist will always need more help than they currently have. Which means that rather than looking around on job websites, you should be looking for Senior Data Scientists you'd like to work with and reaching out to them.
Find a Senior Data Scientist who has the time to guide you
When looking for a Senior Data Scientist to hire you, make sure they have the time to guide you and help you grow. This means that they have the time and space to show you the ropes of the industry as well as the ropes of the data science work that is done in the company. Often times Senior Data Scientists will be overworked because of the amount of projects they have been given and when those results need to be completed. Some Senior Data Scientists will try to do everything on their own and some will try to build an effective team around themselves. You want to find the second type of data scientist as they will already have decided that building a team is the right thing to do and will be willing to invest the time in training and guiding a Junior Data Scientist.
Find a Senior Data Scientist who has the knowledge to guide you
When looking for a Senior Data Scientist to hire you, make sure they have the knowledge to guide you and help you grow. This means that they have not only more advanced statistical, mathematical, computer science knowledge than you, but that they also have better industrial and organizational knowledge than you. Though someone hired should always bring something to the team that was missing before, you want to make sure that it is skewed in you learning something from them rather than them learning something from you and you not learning anything. As you are starting out it should be easier to find someone to learn from, just make sure that they will be teaching you the things that you actually want to learn. Remember, your goal as a Junior Data Scientist is to someday become a Senior Data Scientist, so make sure that you feel that the Senior Data Scientist hiring you will be able to help you become a Senior Data Scientist.
Find a Senior Data Scientist who has the organizational support to guide you
When looking for a Senior Data Scientist to hire you, make sure they have the organizational support to guide you and help you grow. This means that their boss as well as their colleagues from other functional areas in the organization have bought into a) growing the data science team and b) are going to be willing and able to help you get up to speed and be successful at your job. If the Senior Data Scientist is isolated from the rest of the organization, they will have trouble getting the resources to hire you, keep you, help you, reward you, and promote you. If the Senior Data Scientist is well connected within the organization, has the respect of others, and is seen as valuable to the organizational efforts, they will receive all the resources they ask for to help them bring you up to speed and to help you succeed. As a Junior Data Scientist hire, not only are you part of the data science team, you're also part of the company, so you'll want to make sure that you are happy and excited to work with the broader organization.
Find Senior Data Scientists and ask them if they are looking for a Junior Data Scientist
You've started looking for a Junior Data Science job on job websites. Almost all of the jobs you've found posted are from organizations who are looking for senior level data scientists. The problem you're running into is that it's hard to find junior data scientist jobs.
Senior Data Scientists need Junior Data Scientists. You want to find Senior Data Scientist that have decided that building a team is the right thing to do and will be willing to invest the time in training and guiding a Junior Data Scientist. You want to find a Senior Data Scientist who has the time, knowledge, and organizational support to guide you and help you be a success.
The next time you start to look for a Junior Data Scientist position on a job website, close the website and search for Senior Data Scientists instead. You'll get a better feel for the industry, you'll get a better feel for who are Senior Data Scientists, and you'll be able to find great Junior Data Scientist roles that appeal to you and your background / skill set faster. Good luck!