How to avoid RenderFlow error when keyboard appears in Flutter

I am designing a screen with two main sections:

1. A carousel slider with a TextField below it
2. A button

I want the button to be at the bottom of the screen.

To achieve this, I have wrapped the column for 1. in a Flexible widget and set the mainAxisSize for the Column to max, and the mainAxis size for the Column containing the button to min.

Now when I click on the TextField, the keyboard appears, and I receive a Bottom Overflowed error with the Button appearing on top of the TextField.

How do I ensure that the Button stays at the bottom of the screen when the keyboard appears? I have tried wrapping both the Columns in another Column which in turn had been wrapped by a SingleChildScrollView widget, but that overrides the MainAxisSize.max property apparently, and renders the lower Column (containing the Button) just below the upper Column as seen below.

My Code:

class SigninScreen extends StatefulWidget {
  const SigninScreen({super.key});

  @override
  State<SigninScreen> createState() => _SigninScreenState();
}

class _SigninScreenState extends State<SigninScreen> {

  int _currentCarouselIndex = 0;

  List<Widget> indicators(imagesLength, currentIndex) {
    return List<Widget>.generate(imagesLength, (index) {
      return Container(
        margin: EdgeInsets.symmetric(
          vertical: 1.h,
          horizontal: 2,
        ),
        width: currentIndex == index ? 15 : 10,
        height: 3,
        decoration: BoxDecoration(
          color: currentIndex == index ? primary : grey,
          borderRadius: const BorderRadius.all(
            Radius.circular(2),
          ),
        ),
      );
    });
  }

  TextEditingController phoneController = TextEditingController();

  @override
  void dispose() {
    phoneController.dispose(); 
    super.dispose();
  }
  
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: SafeArea(
        child: GestureDetector(
          onTap: (){ FocusManager.instance.primaryFocus?.unfocus();},
          behavior: HitTestBehavior.opaque,
          child: SingleChildScrollView(
            child: Column(
              mainAxisSize: MainAxisSize.min,
              children: [
                Flexible(
                  fit: FlexFit.loose,
                  child: Column(
                    mainAxisSize: MainAxisSize.max,
                    children: [
                      CarouselSlider(
                        items: carouselImageList.map<Widget>((i){
                          return Builder(
                            builder: (context){
                              return Container(
                                width: 100.w,
                                height: 83.w,
                                decoration: BoxDecoration(
                                  image: DecorationImage(image: AssetImage(i), fit: BoxFit.fill),
                                ),
                              );
                            }
                          );
                        }).toList(), 
                        options: CarouselOptions(
                          height: 83.w,
                          aspectRatio: 1/0.83,
                          autoPlay: true,
                          autoPlayInterval: const Duration(seconds: 3),
                          initialPage: 0,
                          viewportFraction: 1,
                          onPageChanged: (index, timed) {
                            setState(() {
                              _currentCarouselIndex = index;
                            });
                          }
                        ),
                      ),
                      SizedBox(height: 1.h,),
                      Row(
                        mainAxisAlignment: MainAxisAlignment.center,
                        children: indicators(
                            carouselImageList.length, _currentCarouselIndex),
                      ),
                      SizedBox(height: 2.h,),
                      Padding(
                        padding: EdgeInsets.symmetric(horizontal: 5.w),
                        child: Column(
                          crossAxisAlignment: CrossAxisAlignment.start,
                          children: [
                            Row(
                              children: [
                                Text(isEnglish ? "Enter your phone number" : "अपना फ़ोन नंबर दर्ज करें", style: globalTextStyle.copyWith(fontSize: 5.w, fontWeight: FontWeight.bold),),
                              ],
                            ),
                            SizedBox(height: 1.h),
                            PhoneNumberField(phoneController: phoneController),
                            SizedBox(height: 1.h),
                            Text(isEnglish ? "OTP will be sent on this number." : "इस नंबर पर ओटीपी भेजा जाएगा।", style: globalTextStyle.copyWith(fontSize: 3.w,),),
                          ],
                        ),
                      ),
                    ],
                  ),
                ),
                Column(
                  mainAxisSize: MainAxisSize.min,
                  children: [
                    CustomButton(width: 90.w, height: 15.w, color: primary, onTap: (){
                      // Navigator.pushNamed(context, otp);
                      (phoneController.text.length == 10) ?
                        Navigator.push(context, MaterialPageRoute(builder: (context) => 
                        OTPScreen(phoneNumber: "+91${phoneController.text}"))) 
                        : ShowSnackbar.showSnackBar(context, isEnglish ? "Enter a valid 10 digit phone number." : "एक मान्य 10 अंकों का फ़ोन नंबर दर्ज करें।");
                    }, text: isEnglish ? "Get OTP" : "ओटीपी प्राप्त करें", fontColor: white, borderColor: primary,),
                    SizedBox(height: 1.h,),
                    Text(isEnglish ? "By signing up, you agree to our Terms and Services" : "साइन अप करके, आप हमारी शर्तों से सहमत होते हैं और सेवाएं", style: globalTextStyle.copyWith(fontSize: 2.5.w,),),
                    SizedBox(height: 2.h,),
                  ],
                ),
              ],
            ),
          ),
        ),
      ),
    );
  }
}

How do I get the Button to stay at the bottom of the screen even when the keyboard appears?