Notice the cost beyond the event
An invitation may occupy an hour on the calendar and require another hour of travel, a changed meal and an arrangement for the children. Before answering, look at the whole shape of the day. Being free at the event's start time does not necessarily mean the plan is easy to manage.
When you are new, it can feel as though every invitation is a rare chance that must be accepted. Some are opportunities you want to take; others arrive in a week that already contains enough. You can decide based on your circumstances without first proving that the event is unimportant.
Give yourself time to check. “Thank you, I will look at the calendar and reply tonight” is clearer than an immediate yes followed by several attempts to rearrange the household. Then reply when you said you would.
Keep the answer straightforward
If you cannot attend, a warm, brief response is usually enough. You do not need to supply a detailed account of your energy, childcare or work arrangements. Thank the person for thinking of you and say that the date does not work.
Offer another option only if you want to make it happen. Suggesting a coffee next week can express continuing interest; repeatedly offering alternatives you cannot manage creates more unfinished planning. It is also fine to say you hope to see them at the next regular group.
If part of an event fits, ask rather than assume. You might be able to come for the first hour or attend without taking on an organising job. Make the limit clear so the host can decide whether that works for the event.
Leave room for invitations you actually want
Look at the pattern over time. If every evening becomes a commitment accepted out of concern about seeming unfriendly, you may have less attention for the connections you most enjoy. A few plans you can be present for may suit you better than constant attendance.
At the same time, do not require a perfect mood or completely empty week before accepting anything. You can choose a small, manageable invitation and see how it feels. The useful distinction is whether you are making a choice, rather than treating every request as a test you must pass to belong.
