Can I do a share purchase if the seller never incorporated the business in the first place?

No — shares only exist for a corporation, so if the seller has been operating as a sole proprietor or an unincorporated partnership, there's no share structure available to buy. The deal has to be structured as an asset purchase instead: you identify and acquire the specific assets, contracts, and, if applicable, employees that make up the business, the same way you would from any seller, incorporated or not.

There's a variation worth knowing about: a seller could incorporate a new corporation first, transfer the business into it, and then sell you its shares instead. This is sometimes done deliberately, often because it can put the seller in a position to potentially access personal tax treatment available on selling qualifying small business corporation shares. But that tax treatment generally has holding-period and asset-use requirements that build up over time, so a corporation freshly created just before a sale may not actually qualify, regardless of what the seller hopes.

If a seller proposes incorporating first specifically to sell you shares, it's worth having your own business lawyer and the seller's accountant confirm that approach genuinely achieves what it's meant to, rather than assuming it works because the idea sounds reasonable.