I get asked this question a lot. Most parents want to know if you must always adhere to a certain structure or system in Phonics and the best way I can answer this question is in two parts.
Firstly, what is it that you want your child to learn? If you're just wanting them to know single sounds and get used to sound differentiation then I would say "Yes, you can wing it!". Now before you get out your pitchforks let me explain.
When you want very young children to learn sounds and make it fun, you teach them one sound at a time. Most of the time you wouldn't have the children sit down and drill them through every single sound. What you'd most likely do is teach a little Phonics with other activities such as arts and crafts, story reading and so forth making sure that you're linking the sound to the book or the thing you're making in arts and crafts.
If you're doing this way then you would have a focus sound for the day/week depending on however many times you're learning sounds. You simply learn the sound and move on to the next sound and revisit it later.
I would start off teaching my children letter Aa. Now keep in mind that you don't have to do this alphabetically but do make sure you keep a note of which sounds/letters you have done already.
I usually spend about a week on each focus sound. This is because I want my children to do more than a few simple activities.
I would start off introducing the children to the letter by using flash cards. I personally teach my children only lowercase letters first as they are more commonly used in English. I would use letter flashcards, tactile cards for finger tracing and then write and wipe cards for simple marking or pencil skills.
Then I would read a book with an object or animal that starts with my focus letter.
So for letter Aa, I would read 'Little Apple Goat' by Caroline Jayne Church.
Once I have completed reading the book I would then make a simple apple art and crafts piece.
(For free apple arts and crafts template below)
Then on the next day I would reintroduce the letter/sound using the flash cards again and then the main activity would be making simple apple pies.
You don't have to revisit the sounds everyday but the more practice the children have the faster they will learn. I would say three times a week is plenty for very young children.
For the second part of my answer I would say "No, you can't wing it" and this is because if you're talking about children who are about to transition into school or already in school, they aren't only learning to recognize the individual sound but to also recall the letters as well as learning to blend and segment the sound in word.
Due to a higher requirement of understanding, it is better to approach Phonics learning for reading and writing in a methodical and systematic order.
There are many Phonics systems for you to choose from. It's really up to you which approach you'd like to use. However please do keep in mind that once you pick one, you should stick to it and not dabble in other systems. This is because it'll be counter productive to your child's learning as each system follows a different letter/sound learning order.
So just a conclusion about winging it, you can for very young children learning sound differentiation but you can't wing it for children who are learning Phonics for reading and writing skill development.
It's important to remember to stick to a systematic order and to make it fun! Children learn the most when they are enjoying themselves.