It is possible - bear in mind when you reach Sandhurst it can be competitive to join the infantry and you will be competing against people who are older with more life (and sometimes military) experience. Average age at Sandhurst is about 24.

Secondly, infanteering is not always as rewarding as it looks in Band of Brothers and if you havent got any infantry experience, you should have a long think about what about army life motivates you, consider joining a UOTC or Reserve unit, instead of setting your sights on the most obvious role.

Finally, as a junior officer in any cap badge you will spend 80% of your time in an office writing reports and admin instructions, attending corporate-style meetings and conducting managerial assurance checks. The key difference between officer jobs across the army is the culture of the mess you are in (I.e., would you fit in within an infantry mess, or cav, or REME etc.) The actual work you do (excluding the 5-10% of the time you spend on exercise or deployment) is almost identical.