Advice on how to help my beech hedge up

Yes, provided that that some branches stick out far enough (more than 2' say) - and I would only prune those now - I would remove [just] the tip of every branch during the Winter

Same again next year / first 3 or 4 years life - by which time it will be getting too big to be able to do that! and you'll be using sheers on the sides to "roughly trim it" to the width you want, and then you will be taking out the top (let it grow 1' taller than desired height, then cut it back to 6" below finished height (secateurs, cutting individual stems; that will make the top bush-out to the final height) then the following year just cut it with hedge trimmer / shears to final height. By then you will probably be cutting the sides with hedge trimmer to - top 20% may still be a bit thin, but the bottom should be well developed and about as thick as it is ever going to be - it will thicken up a bit thereafter, but if it is full of gaps they won't cure and will need some remedial pruning