You will 100% still be able to achieve your goals without a gym
You don't need all the fancy gym equipment in order to see results. What will ultimately help you see results is
1. Consistency: You can't expect to see results without putting in the work.
2. Effort: You should be performing at a level where you're at least 1-3 reps short of the point where you could not possibly do 1 more rep with proper form. There's a difference between a mental block of (I don't think I could do more) and a physical block of (My body cannot perform more). The mental block may be the reason why some people believe they are 1-3 reps left but in reality they are capable of doing another 5-7 reps.
3. Volume: Can be thought as how many sets is being loaded per muscle group per week. Although this is variable among individuals, this is why working with our coach will eliminate that guess work as they will know the appropriate amount of volume you need to see muscle growth.
4. Execution: Good technique and form is fundamental to seeing success (and reducing risk for injuries). You shouldn't be "going through the motion", "using momentum", or "doing partial range of motion". With ongoing form checks with your coach they will ensure you are performing at your peak level.