It is possible to do this in plain C. Adobe did it. Artifex did it. Others have done it. But as commented, it is a ton of work. But I can outline the steps to give you a feel for what's involved.

First you could read the "Magic Number" at the start and check that it is actually a PDF. It should start with %PDF- followed by a version number. But apparently many PDF producers don't conform to this requirement.

Next, you need to skip to the very end of the file and read backwards, looking for something like:

startxref
1581
%%EOF

That number is the byte-offset of the start of the X-Reference table which lists the binary offsets of all the "objects" in the file. An object can be a Page or a Font or a Content Stream or many other things.

Looking at the X-Reference table, you'll see something like this:

xref
0 4
0000000000 65535 f 
0000000010 00000 n 
0000000063 00000 n 
0000000127 00000 n 
0000000234 00000 n 
trailer
<<
  /Root 1 0 R
  /Size 4
>>

The line /Root 1 0 R tells you which object is the root of the document tree. You'll need to examine this object to find the top-level Pages object which looks like this:

2 0 obj
<< /Kids [ 3 0 R ] 
/Type /Pages 
/Count 1 
>> 
endobj

The Kids element here contains a reference to the first Page object which looks like this:

3 0 obj
<< /Contents [ 4 0 R ] 
/MediaBox [ 0.0 0.0 612.0 792.0 ] 
/Type /Page 
/Parent 2 0 R 
>> 
endobj

Then you'll need to find the Contents object referenced here. A Content stream, if it's not encrypted or compressed, will show you the drawing commands and text commands being drawn to the page.

5 0 obj
<<
  /Length 15660 
>>
stream
BT F1 10.0 Tf 30.0 750.0 Td (<< ) Tj ET BT F1 10.0 Tf 50.0 738.0 Td (/) 
Tj ET BT F1 10.0 Tf 56.0586 738.0 Td (astring) Tj ET BT F1 10.0 Tf 86.7852 
738.0 Td ( ) Tj ET BT F1 10.0 Tf 89.2852 738.0 Td (\() Tj ET BT F1 10.0 Tf 
92.6133 738.0 Td (this string data) Tj ET 
[...lots more commands follow...]
endstream
endobj

Text commands will always be bracketed by BT ... ET. In here, you can finally see the strings wrapped in parens. But you'll have to pay attention to the coordinates 30.0 750.0 Td of each string to figure out which ones are part of the same logical line.

If the PDF was created from a word processor, it is likely to contain text in this form but with lots of caveats. It might have re-encoded fonts and the text strings will no longer represent ASCII characters but just positions in the font's encoding vector. If the PDF was created from a scanned document, it may just contain images of the pages with no text content at all unless it has gone through a conversion involving OCR.