The first meeting will explore design ideas by a 'walk and talk' on site and comparison to relevant previous projects from the portfolio, showing how other clients have arrived at their own preferred design solutions and what their budgets were.
The initial meeting does not normally generate any sketches or specific design proposals as such as it is often too early to commit to a design solution without first fully understanding the site, emerging brief, and budget.
The introductory meeting covers a discussion of your initial brief and any ideas and issues arising, together with an overview of the stages of a typical building project from inception (start) to completion (finish) including Planning (or a Permitted Development 'Certificate of Lawfulness'), Building Control and construction operations on site under a building contract. This overview is particularly useful if you have no previous experience of building work.
The actual design itself will emerge during the later design process or Concept Design (Stage 1-2) after the formal appointment to proceed. This will usually develop more than one option to consider, perhaps smaller and larger schemes for comparison, before refinement towards a final preferred scheme for Planning and costing.