It depends on what you really want to do in the future. Learning a framework could be useless if you don't know how to do correctly basic things as creating a train, test and validation set.

There are basic things I think you must know before jumping into a framework or int any specific algorithm. First thing you probably will have to do is to collect the data and clean it. In order to do this correctly you need some basic statistics. For example you need to know what is a gaussian distribution and collect samples in a way that are representative of your problem. Then you may need to clean the samples, remove outlines, complete blank data, etc. So it is basic you know some statistics to do this right.I have seem people with a lot of knowledge of tools than then they are not able to create a train/test/validation set correctly and the experiment is completely invalid from here no matter what you do next (http://stats.stackexchange.com/questions/152907/how-do-you-u..., https://www.youtube.com/watch?v=S06JpVoNaA0&feature=youtu.be ). You also need to know how are you going to test your results, so again you need to know how to use a statistical test (f-test, t-test). So first thing, jump into statistics to understand your data.

The next step I think is to know some common things in machine learning as the no free lunch theorem, curse of dimensionality, overfitting, feature selection, how to select the current metric to asses your model and common pitfalls. I think the only way to learn this is reading a lot about machine learning and making mistakes by your own. At least now you have some things to search in google an start learning.

The third step would be to understand some basic algorithms and get the feeling of the type of algorithms, so you know when a clustering algorithm is needed or your problem is related classification or with prediction. Sometimes a simple random forest algorithm or logistic regression is enough for your problem and you don't need to use tensorflow at all.

Once you know the landscape of the algorithms I think it is time to improve your maths skills and try to understand better how the algorithms works internally. You might not need to know how a deep network works completely, but you should understand how a neural network works and how backpropagation works. The same with algorithms as k-means, ID3, A*, montecarlo tree search or most popular algorithms that you are probably are going to use in day to day work. In any case you are going to need to learn some calculus and algebra. Vectors, matrix and differential equations are almost everywhere.

You would probably have seen some examples when learning all the stuff I talked about, then it is time to go to real examples. Go to kaggle and read some tutorials, read articles about how the community of kaggle has faced and winning the competitions. From here is just practice and read.

You can jump directly into a framework, learn to use it, have 99% accuracy in your test and 0% accuracy with real data. This is the most probably scenario if you skip the basic things of machine learning. I have seen people doing this and end up very frustrated because they don't understand how their awesome model with 99% accuracy doesn't work in the real world. I have also seen people using very complex things as tensorflow with problems that can be solved with linear regression. Machine learning is a very broad area and you need maths and statistics for sure. Learn a framework is useless if you don't understand how to use it and it might lead you to frustration.