I'm confused, do you want to become a data engineer or a data scientist? A data scientist is a type of senior data analyst. Data engineering is farther away to a data scientist than a data analyst is.

I'm going to answer both questions just in case:

To become a data engineer / infrastructure engineer, there are multiple paths forward. I recommend doing BI work aka Business Intelligence Analyst Engineer. It's typically Tableau related work, so making dashboards and reports for management. It's still a data related role so you should feel comfortable and at home. However, it is also an engineering role. If you're the first BI at a company you'll often find yourself setting up an SQL server and doing certain data engineer-light type work to get data into the server. You'll need to set all of this up, so BI is a blend of data engineering and data analyst type work.

Once you've gotten familiar with BI work it's very easy to transfer to data engineer / infrastructure engineer type work. This is especially true if you end up setting up a data warehouse (as an alternative to MySQL) or data lake on AWS to do your BI work. You don't have to, but if you go that far, you're pretty much doing data engineering at that point. The line between the two is fuzzy. Data engineers and infrastructure engineers are expected to be architects, and by that I mean they are expected to future proof the schema of the SQL server / data warehouse (future proof setting up the database for new data so it doesn't become a mess). A BI is not expected to be an architect and imo the only way to gain that skill is through first hand experience playing with databases, so a BI is a good way to get that experience.

At the current company I'm at the infrastructure engineers are expected to do BI work. This is unusual as the data scientists typically do it (roughly 60% of data scientists do BI work), because one of the data engineers I currently work with was a BI at his previous job. (He was on the sales team, helping them with more than just dashboards, like helping with their Excel spreadsheet algorithms and what not.)

I'm sure others could paint another path forward. Data engineers are highly in demand so it could be as simple as applying. If you can pass a white board interview (leetcode style interview) you can skip this step and dive right on in. Just like any technical white collar job, you're expected to self-learn what is required for the job before going in, so absolutely read guides / take classes / read books / etc on the topic to learn more.

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To get a job as a data scientist:

BI work is a good bridge too, but not in learning setting up database skills, but creating dashboard skills. Around 60% of data scientists in the industry do BI work. Me, I've had to create internal dashboards for diagnosing problems, so it streams in live data in a visual way. This is not BI work, but there is clearly a bridge between BI dashboards and internal diagnostics dashboards.

Technically a data scientist is a kind of data analyst so many people go from data analyst directly to data scientist. Around 30% or so of data scientists do only data analyst work but have the data science title. (This 30% number is a bit of an estimate.) It's that strong of an overlap.

Data scientists tend to specialize. There sales data scientist, a marketing data scientist, an engineering data scientist, ops data science, and so on. Often times, but not always, they sit on the team they specialize in, instead of on a data science / data analyst team. At smaller companies they tend to hire a data scientist and expect them to do one kind of role. So it comes down to what kind of data science work you want to do. Sales data science roles tend to be BI heavy. Marketing data science roles tend to be data analyst heavy. Engineering data science roles tend to be the heavy model building roles that are the most challenging out of the bunch. Ops data scientists tend to specialize in malware detection and self-reporting. Eg, if someone is hacking the company's servers, they might get notified of an alert, and then they analyze it and report on it. There are other kinds of data scientists, like ones at super market companies and restaurants that specialize in forecasting warehouse items.

Me, I'm a specialist that specializes in robotics and sensor analysis. I'm not going to lie, it's probably the hardest out of every kind of data science role. It's very heavy on the engineering side, not data engineering, but software engineering, because there is a lot of advanced feature engineering.

Most feature engineering is simple stuff like deleting missing values, performing the medium over the dataset or other kinds of cleaning and minor modifications like normalizing the data. Then it gets spit into an ml library that identifies the pattern in the data, so when new data comes in it can identify if it recognizes that pattern. Each pattern is called a category and most ML work is categorization, so maybe you're categorizing different kinds of customers and if you can identify a pattern in their shopping habits, you might be able to predict what they will buy next.

Advanced feature engineering might need to be used when your patterns are so complex ML can't pattern match it well, so you have to give it a helping hand and manually do some of the pattern matching. I've also had to invent new forms of ML too, but it's been a while since I've had to go that far. What I do is the farthest from normal for data science.

Most data scientists do not know advanced feature engineering, but it's one of the bridges between software engineering and data science, so leveling up software engineering can help on that front. (Which is also why I bring it up.)

A data scientist shouldn't be expected to know much or any data engineering skills. Instead, gaining managing upward skills helps. How to do an sql query to get data and how to write a join is enough. You should do fine, just try learning data science itself instead of learning data engineering, unless you're curious. (A lot of universities and bootcamps teach machine learning engineer skills and call it data science. If it doesn't have data cleaning and feature engineer, it's probably not data science. Likewise if it has tensorflow or pytorch in it, it's not data science.)