Hello,
You can apply to a polytechnic institute only after, you passed your 10th class. But let me tell you that, different polytechnic institutes have different eligibility criteria for admission. Some polytechnic colleges take entrance test, while some provide direct admission on the basis of 10th marks.
So, if you are willing to take admission in some particular polytechnic college, then please read its eligibility criteria first. You can easily find the eligibility criteria on their official website.
Also, after completing the polytechnic, you can get admission to B.Tech courses as lateral entry student.
Hope it helps.