hiya Mia,
great to hear about a kitty learning to share outdoor time with owner from a young age.
I took my girl out as soon as she was safe (vaccinated) and only stopped while she went thru her spay and recovery.
At first Cleo trembled and froze.. and would kinda lay on her side and look at me all scared.
For the first few times (and in garden not the street) just being outside is enough... you need to try to end the outdoor sessions on a positive and not due to bolting indoors from fear.
I started out by carrying kitten Cleo outside and crouching down onto one knee and placing her under me... (a natural defensive posture for mommy cat and kitten) and Cleo would just sniff and look around and feel the breeze on her ect... a few minutes is all that needs at first... then back in with no drama harness straight off and some nice back rubs and grooming.
(or you could try taking him out in his carrier and just open the door ... no force or pressure to leave the carrier unless he wants to - but give the option)
After a few times of going out and feeling protected and coming back in your kitty should realise there is no danger and gain confidence... venturing out from your safezone (underneath you or out of his carrier) and again its important to go gradually to try to always end the session on a good note... sometimes a noisy car nearby or a plane overhead can be scary and set you back ... but persevere.
Another thing, be sure YOU stay calm and confident in tone and posture so kitty can pick that up - make sure you are always in sight of him (when he is later exploring around) and also that the entrance back into the house is always in sight and open, dont close the door to the house while you are out and stay close to it.
Think of how you started with one room being a ''saferoom'' in your house and introducing new rooms only with this the house itself is the ''saferoom'' and the garden is a new ''room'' to introduce gradually as confidence grows.
good luck, please share your story and any piccies would be awesome
(click my Sig to see vids of my girl out on walkies)