Context, pictures, sentence structure come in here IMO at the earliest stages (without undermining phonics).
But unfortunately they do undermine phonics.
One of the most important, and frequently overlooked, skills for reading is the development of the eye tracking muscles. For fluent reading the eye muscles must be 'trained' to scan from left to right, all through each word It doesn't come naturally, reading being a 'unnatural' skill. If the development of tracking is impeded by constantly looking away from the words to scan the pictures you are likely to end up with a child who misses words out, reads words from back to front, can't keep their place in the text and who finds 'correct' reading physically tiring because of the strain on poorly developed muscles. Phonics teaching, with its emphasis on left to right tracking all through the word, from word to word all through a sentence, is the best exercise for strenthening tracking muscles.
Context is not always reliable for identifying what a word 'says' (and why would you need it, anyway, if you can decode the word?). Context is more useful for possibly working out the meaning of a word, but a dictionary is more accurate and reliable, or a definition given by someone more knowledgeable...
Early texts are not complex or challenging to a child's understanding; they will only have a problem with 'meaning' if a word, or words, they encounter are not in their expressive (spoken) or receptive (words spoken to them) vocabulary. This is a language problem, not a reading one. This is why good phonics teaching is always set within a rich language context, with lots of speaking and listening and having good literature read to children. This is why it is important to talk to your child and read to your child; it develops the language and vocabulary which will help them to understand and enjoy the more complex texts they can read once the basic phonic skills are in place.