Get the website up first, and as long as your margins are good, you can allow for extra delivery time upfront, as long as you let your customers know when they can expect to receive their orders.
If you are concerned about this, you could pre-order the top two or three items you think will sell most and have those on hand, but keep in mind that the whole idea behind many online ventures is to keep a limited amount of stock on hand.
That said, continue looking for a good drop-shipper you can work with. There are many who would be amenable. Just make sure you can
keep your margins where they need to be, and that you are not paying retail for something that should be priced wholesale or better.
All the best.
Brad Sugars
Brad Sugars is the founder of ActionCOACH, the world's number one business coaching firm. As a world-renowned entrepreneur, author and Business Coach, he has helped more than a million clients around the world find business and personal success.
Sugars has owned and operated more than two dozen companies including his main company, ActionCOACH, which has nearly 1,000 offices in 26 countries.